Archive:New Draft of the Week

The New Draft of the Week is a chance to highlight a recently created Citizendium article that has just started down the road of becoming a Citizendium masterpiece.
It is chosen each week by vote in a manner similar to that of its sister project, the Article of the Week.

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To add a new nominee or vote for an existing nominee, click edit for this section and follow the instructions

Table of Nominees

Nominated article	Vote Score	Supporters	Specialist supporters	Date created
The Sporting Life (album)	2	Meg Ireland; Drew R. Smith		2009-07-21
The Dead Weather	1	Drew R. Smith		2009-07-15
Screaming Lord Sutch	1	Howard C. Berkowitz		2009-07-24
The Rolling Stones	1	Daniel Mietchen		2009-07-28

If you want to see how these nominees will look on the CZ home page (if selected as a winner), scroll down a little bit.

Recently created pages are listed on Special:NewPages.

Transclusion of the above nominees (to be done by an Administrator)

• Transclude each of the nominees in the above "Table of Nominee" as per the instructions at Template:Featured Article Candidate.
• Then add the transcluded article to the list in the next section below, using the {{Featured Article Candidate}} template.

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The next New Draft of the Week will be the article with the most votes at 1 AM UTC on Thursday, 6 August 2009. I did the honors this time. Milton Beychok 01:02, 30 July 2009 (UTC)

Nominated article	Supporters	Specialist supporters	Dates	Score
The Dead Weather: An American Alternative Rock band formed in Nashville, Tennessee in 2009. [e] The Dead Weather is a "a death-rattle blues quartet" formed in Nashville, Tennessee in 2009. Formed by Jack White of the White Stripes and the Raconteurs, the band is comprised of VV (Alison Mosshart) of the Kills, on guitar and vocals; Dean Fertita of Queens of the Stone Age, on guitar and organ; Little Jack (Jack Lawrence) of the Raconteurs and the Greenhornes, on bass; and Jack White on drums and vocals. The band was revealed, and performed for the first time, at the opening of Third Man Records' Nashville headquarters on March 11, 2009, immediately before releasing their debut single "Hang You from the Heavens". Band members Jack White Jack White formed the White Stripes in 1997, and they went on to have a string of critically acclaimed albums, with their third, White Blood Cells, catapulting them to international stardom. In 2005, White became a founding member of the rock band the Raconteurs. In 2009, he became a founding member of his third group, the Dead Weather. Jack White plays drums, and provides vocals for the Dead Weather. Alison Mosshart "VV" Alison Mosshart started her musical career in 1995 with the Florida punk rock outfit Discount, which disbanded in 2000. She then co-founded the Kills with British guitarist Jamie Hince in 2000. Alison Mosshart plays guitar and provides vocals for the Dead Weather. (Read more...)	Drew R. Smith		1
The Sporting Life (album): A 1994 studio album recorded by Diamanda Galás and John Paul Jones. [e] This article may be deleted soon. To oppose or discuss a nomination, please go to CZ:Proposed for deletion and follow the instructions. For the monthly nomination lists, see Category:Articles for deletion. The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] The Sporting Life Image:SportingLifealbum1994.jpg Type Studio album Artist Diamanda Galás and John Paul Jones Release Date 6 September 1994 (US), 1 October 1994 (UK) Recorded 1994 at AIR Studios, London. Mastered at Metropolis Mastering, London. Genre Alternative rock, experimental rock Language English Length 55 minutes 4 seconds Label Mute Records Catalogue Mute 61672 (US), Mute STUMM 127 (UK) Producer John Paul Jones Engineer Richard Evans The Sporting Life (album)|The Sporting Life is an album by avant-garde singer Diamanda Galás and multi-instrumentalist John Paul Jones, released on 6 September 1994, on Mute Records. It is Galás' sixth studio album, produced by Jones. Overview The record was a notable shift in musical style from what was previously produced with Galás. The album's subject material incorporated various lyrical themes such as lust, revenge, violence, murder, betrayal, and death, mixed with sarcasm and dark humour. Galás' previous work centred around the theme of AIDS and subsequent deaths from it, after her brother and some of her friends succumbed to the disease. This album was a change in direction, albeit a much more commercially accessible one, with the additional input of former Led Zeppelin bass player and keyboardist John Paul Jones on songwriting, performance and production duties. Jones was working on a live project with Heart (band)|Heart at the time of this collaboration. When interviewed about his involvement Jones explained: ‘ I was immediately impressed with her voice, and the power and the emotion. Our backgrounds are very similar. We both played in our fathers' bands when we were starting out, and we're both great fans of classical music, jazz, blues, Mediterranean music and Arabic music. A mutual friend suggested that we should work together, and I think she wanted to do a Rock music ’ —rock record. Jones had previously been introduced to Galás' body of work in 1983 via his wife Maureen, who brought home and played a 1982 compact disc containing 'Wild Women with Steak Knives (The Homicidal Love Song for Solo Scream)'. Galás intimated in an interview with online magazine Convulsion that she wanted to explore other facets of life outside of the AIDS epidemic, such as 'sick relationships.' The 'sporting life' is street hustler slang for the place where affection is a commodity, where the only love that's not for sale is obsessive and destructive love. Writing and composition After an initial evening meeting in London where they both agreed to work together, the album was composed both in New York (disambiguation)|New York (Galás) and in England (Jones). Demo tapes were exchanged, with Jones providing compositional ideas on an 8 string bass, while Galás added organ and lyrics to them. This continued until they were both satisfied with the material and a rehearsal arranged. The recording process took three weeks in London, in which Thomas laid down drum tracks in the third and final week. With mixing, the entire project took two months in total. Galás described the project as a collection of homicidal love songs: ‘ I think that if you get together and decide to do an album called Homicidal Love Songs, which is what I originally wanted to call it, you've got to have a sense of humor. What makes this album possible in terms of lyrics is real life experience. Every single song, and John [Paul Jones] knows it, too, has a particular person in mind with whom I have had various provocations and entanglements. ’ On the recording, Galás utilises both Hammond B3 organ and piano. The drummer used for the album was Pete Thomas, from Elvis Costello's backing band the Attractions. Due to his commitments with The Attractions, former Heart drummer Denny Fongheiser performed in place of Thomas for subsequent live appearances. Galás has a 3½ octave vocal range which she uses to full effect on the album. Jones commented that 'With a voice like Diamanda's, a guitar would simply be a cosmetic device.' The album opens with 'Skótoseme' which is Greek for 'kill me', on which Galás meshes her frantic, operatic voice with Jones' funky bass lines. A merging of heavy rock and Ancient Greek tragedy. The song 'Do You Take This Man?' mocks wedding vows by comparing romance to imprisonment, where the only solution is submission. Galás' haunting cover of Percy Sledge's soul classic 'Dark End of the Street,' reminds lovers that death is not far away. The title track 'The Sporting Life' meanwhile, tells the tale of a group of prostitutes who stalk and kill a man for fun. Death laments melt into Hammond-driven Cajun dance music on 'You're Mine'. 'Last Man Down', is a wailing blues drenched song about isolation and despair, with lap steel guitar embellishment. Release and critical reception Image:Thesportinglifepromo.jpg|thumb|200px|right|A screenshot from the music video, depicting Diamanda Galás and John Paul Jones. Alternate cover picture outtakes with Galás and Jones in a convertible, with Jones driving, appeared in a 1994 issue of Musician (magazine)|Musician magazine. One of these images was used for the CD single cover of 'Do You Take This Man?' A video was filmed for the single and was completed on 29 July 1994, with director Jon Reiss. It featured Galás in various scenes throughout New York, with Jones playing an eight string bass guitar, and released on 22 August 1994 prior to the album launch. Jones also used 4, 5, and 6 string basses plus a lap steel guitar, while the pair toured throughout October 1994 - January 1995 to promote the album, with concerts billed as 'An Evening of Homicidal Love Songs.' This was Jones' first full tour since Led Zeppelin's 1980 Tour Over Europe 1980|Over Europe tour. The album was released to mixed reviews. Entertainment Weekly offered the most positive with a B+ rating: '... Led Zeppelin bassist Jones and Pete Thomas join the demonic diva to form a power-mad trio on Galas' most rocking album yet ...' while Musician magazine went further: '... At times, The Sporting Life sounds like the best album Led Zeppelin never made, with Galas' acrobatic, banshee-giving-birth caterwaul subbing for Jimmy Page feedback in a newfangled power trio ...' Bomb (magazine)|Bomb arts magazine described it as: '... An expanse where divisions between what is electronic and what is "natural" smear, where the instrument is only as good as its ability to scalp you ...' Track list Album information 1994 Vinyl listing: Side One: 'Skótoseme' (Diamanda Galás, John Paul Jones) – 6:27 'Do You Take This Man?' (Diamanda Galás, John Paul Jones) – 6:09 'The Dark End of the Street' (Chips Moman, Dan Penn) – 2:43 'You're Man' (Diamanda Galás) – 5:10 'Tony' (Diamanda Galás) – 5:37 Side Two: 'Devil's Rodeo' (Diamanda Galás, John Paul Jones, Pete Thomas) – 5:37 'The Sporting Life' (Diamanda Galás, John Paul Jones) – 5:45 'Baby's Insane' (Diamanda Galás) – 4:39 'Last Man Down' (Diamanda Galás, John Paul Jones) - 4:50 'Hex' (Diamanda Galás, John Paul Jones) - 8:04 Chart positions Album Chart (1994) Peak position US Billboard The 200 Albums Chart — Singles Year Single Chart Position 1994 'Do You Take This Man?' US Billboard Hot 100 Chart — Credits Personnel Musicians: Diamanda Galás – vocals, keyboards John Paul Jones – bass guitar, electric guitars, keyboards, piano, bass pedals, producer Pete Thomas - drums, percussion Production: Richard Evans – engineer, mixing Tim Young - mastering engineer Patricia Mooney - art direction Catherine McGann - photography Notes  (Read more...) Meg Ireland; Drew R. Smith 2  Screaming Lord Sutch: (10 November 1940 - 16 June 1999), English singer and politician, leader of the Official Monster Raving Loony Party. [e] The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] Screaming Lord Sutch, 3rd Earl of Harrow (born David Edward Sutch, 10 November 1940 - 16 June 1999) was an English musician and politician. As founder of the Official Monster Raving Loony Party, he was the longest serving leader of a British political party. Career Sutch was born at New End Hospital, Hampstead, North West London, and grew up in the working class area of Kilburn, North London. His father, a policeman, was killed in the Blitz, while his mother worked as a cleaner. Sutch fell in love with rock 'n' roll upon hearing 'Rock Around the Clock' in 1956 on his crystal radio set. His earliest public performances were at a local biker hangout called the Cannibal Pot Coffee Bar, on Harrow Road. Inspired by one of his favourite rock and roll stars, Screaming Jay Hawkins, he changed his name to Screaming Lord Sutch, 3rd Earl of Harrow. Despite the fact that he had no connection with the peerage, the deed poll laws of England at the time permitted this. He was one of the first musicians in England in the 1960s with long hair, reputedly 18 inches long, a fashion statement of rebellion that soon caught on with other rock artists. Sutch was aware of his weaknesses as a melodic vocalist, and relied heavily on image, taking his lead from Screaming Jay Hawkins, and putting on a show that mixed rock 'n' roll, theatrics and gothic horror. Among the stage-props he used were an axe, daggers, skulls and a black coffin he emerged from dressed as Jack the Ripper. In 1961 while playing at London, United Kingdom's famed 2 I's coffee bar in Soho, he was discovered by maverick producer Joe Meek. Sutch then assembled his first backing group, the Raving Savages. Recording at Meek's home studio in Holloway Road, Islington, Sutch and the Savages often had their records banned by the BBC, a fact which only served to give them more publicity and notoriety. Although never achieving any hit records, the Savages were an accomplished live band featuring Ritchie Blackmore, Andy Wren, and Carlo Little. Their early releases include 'Til the Following Night' (their debut a-side), 'Jack the Ripper', 'Dracula's Daughter', and 'I'm a Hog for You Baby'. Sutch once changed the name of the band to Lord Caesar Sutch & the Roman Empire, with his band dressed as Roman soldiers and Sutch dressed in a toga riding around to gigs in a horse drawn chariot, although this did not last long. Sutch's relationship with Meek ended when the two fell out over money that Sutch claimed Meek owed him. The Savages went through numerous line-up changes throughout the 1960s, including the departure of guitarist Blackmore who later went on to form Deep Purple. In January 1968, Sutch left England to tour and establish himself in the United States of America, and for most of the late 1960s and early 1970s spent increasing time living in Los Angeles. During Led Zeppelin's Spring tour of the US in 1969, he met with manager Peter Grant, whom he persuaded to assist him in brokering a recording deal with Atlantic Records. Sutch also met guitarist Jimmy Page, who was scouting studios to record in during their tour, and managed to get Page and John Bonham to test the facilities at studio Mirror Sounds in May 1969, by recording a number of rock standards. He later secretly recorded a set of his own lyrics over the standards they performed. Sutch enjoyed minor success in 1970 with the album Lord Sutch and Heavy Friends, which featured Page, Bonham, Jeff Beck, Nicky Hopkins, and Noel Redding. The musicians involved were however unimpressed with Sutch, believing the recordings to be for a studio test only. In 1971, Sutch assembled a new line-up for the Carshalton Park Rock 'n' Roll Festival, and had the evening secretly taped. This later appeared in 1972 as Hands of Jack the Ripper featuring Keith Moon, Ritchie Blackmore, and Nick Simper, but it failed to chart. To promote his albums, Sutch toured the United States of America in a Union Jack painted 1955 Rolls Royce Silver Wraith. In 1972, he was also arrested and later released without charge, when he accompanied five naked women to Downing Street to protest at the shortage of rock music on the BBC. He recorded his final album Alive & Well in 1980, featuring Pat Travers, Rick Nielsen, and Klaus Voormann. Numerous compilation albums have proliferated after the 1980s. Pirate radio In May 1964, taking advantage of a loophole in the UK broadcast law, he founded Radio Sutch, one of the first pirate radio stations in Britain, often playing his own records and those of his friends, with late night readings of a bawdy nature. Early broadcasts were transmitted from The Cornucopia, a fishing trawler, and were fraught with technical problems. The vessel was used in the early morning for fishing, and after midday it would begin broadcasting its programmes. The station finally moved to Shivering Sands, a disused wartime fort, located in the Thames Estuary off Southend. Now in competition with the newly launched Radio Caroline and hampered by a weaker transmission signal to London, Sutch began losing interest in the venture and he sold the station in September of that year to his manager Reg Calvert, who re-launched it as Radio City. Political aspirations In 1963, Sutch made his first foray into politics, standing as a parliamentary candidate (as Lord Sutch) for his own National Teenage Party (NTP) in Stratford-Upon-Avon. Straford-Upon-Avon was previously held by conservative MP John Profumo, who had to resign over the Profumo Affair. The NTP's platform included reducing the voting age to 18, establishing commercial radio, abolition of the 11-plus exams, and all-day opening of pubs, all of which have since become law in Britain. Sutch received a mere 208 votes but his taste for politics had been whetted and over the next 30 years he stood in 40 elections - more than any other candidate in history, and earning him a place in the Guinness Book of Records. As founder of the Monster Raving Loony Party, which replaced the NTP, he eventually became the longest surviving leader of any UK political party, despite the fact that he lost his own deposit at every election. In total, Sutch stood for Parliament 39 times, plus 1 Euro-election in 1989, polling some 15,000 votes, forfeiting more than £10,000 in lost deposits and incurring £85,000 in campaign expenses. Sutch formerly registered the Monster Raving Loony Party in 1983, and campaigned for more than one Monopolies Commission, for the European butter mountain to be turned into a ski slope, and to breed fish in the wine lake, 'so they'd come out ready pickled!' Sutch would appear during campaigns with his trademark megaphone, top hat and leopardskin shirt. The party's official slogan was: 'Vote for insanity, you know it makes sense'. In the ITV comedy series The New Statesman, he appeared as himself in the 1987 elections, securing second place against the SDP and Labour candidates. A Heineken Pilsener commercial in the 1990s featured Sutch as Prime Minister at 10 Downing Street. In 1991 Sutch published his autobiography Life As Sutch (with Peter Chippendale) published by Harper-Collins. Sutch's strongest showing was at Rotherham in May 1994 when he polled 1,114 votes, only some 200 short of the number required for saving his deposit. His most significant result, however, was at Bootle in May 1990, when he scored 418 votes to the Social Democrats' 155, a result which helped to convince Dr David Owen that his party was finished. In 1995, Sutch was facing bankruptcy when Barclays Bank threatened to foreclose on a loan of £194,000, but William Hill, the bookmakers agreed to finance his election deposits, and the bank re-scheduled his repayments, so that in July he was able to record one of his best results (782 votes) at the Littleborough and Saddleworth by-election. In the 1997 general election, English betting agency Ladbrokes gave odds of fifteen million to one against Sutch ever being Prime Minister of England, their greatest odds ever. They only gave fourteen million to one against little green men being found on Mars. Although he didn't win the seat, Sutch in the end scored 10 times the vote of Dr Alan Sked's UK Independence Party. It would also prove to be the party's final national election campaign as Sutch could no longer afford the deposits, which had been increased for every candidate from £150 to £500. Death Despite his seemingly light-hearted antics, Sutch in reality suffered from periods of depression and committed suicide by hanging himself at home on 16 June 1999, affected by the sudden death of his mother Annie Emily Sutch in late 1997. He had been previously booked to appear at a show in Las Vegas, and tour the US. At the coroner's inquest into his death, his fiancée Yvonne Elwood stated that he had 'manic depression'. Indeed, her descriptions, both of his symptoms and their treatment by doctors with antidepressants, suggest that Sutch suffered from clinical depression. Sutch never married, but is survived by a son, Tristan Lord Gwynne Sutch, born in 1975 to the American model Thann Rendessy. Party chairman Alan 'Howlin Laud' Hope, took over as Monster Raving Loony Party leader after Sutch's death. A spokesman for Prime Minister Tony Blair stated: Screaming Lord Sutch will be much missed. For many years he made a unique contribution to British politics. Our elections will never be quite the same without him. The 2008 Joe Meek biopic Telstar featured singer Justin Hawkins as Screaming Lord Sutch. Notes  (Read more...) Howard C. Berkowitz 1  The Rolling Stones: Famous and influential English blues rock group formed in 1962, known for their albums Let It Bleed and Sticky Fingers, and songs '(I Can't Get No) Satisfaction' and 'Start Me Up'. [e] The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] The Rolling Stones Years active 1962– Status Active Origin London, United Kingdom, England Music genre(s) Blues rock, rock Members Brian Jones (1962-1969) Mick Jagger Keith Richards Bill Wyman (1962-1993) Charlie Watts Ian Stewart (1962-1985) Mick Taylor (1969-1975) Ron Wood Chuck Leavell The Rolling Stones are a highly successful and influential English blues-rock band, and self-styled 'Greatest rock 'n' roll band in the world. The long-running songwriting partnership of Mick Jagger and Keith Richards (dubbed the Glimmer Twins) rivals the Beatles' John Lennon and Paul McCartney in popularity and chart hits. Band history Origins Originally billed as the Rollin' Stones, the first line-up of this English 1960s group was a nucleus of Mick Jagger (b. 1943, vocals), Keith Richard (b. Keith Richards, 1943, guitar), Brian Jones (1942-1969, rhythm guitar) and Ian Stewart (1938-1985, piano). Jagger and Richard were primary school friends who resumed their camaraderie in their closing teenage years after finding they had a mutual love for R&B and particularly the music of Chuck Berry, Muddy Waters and Bo Diddley. Legend has them bumping into each other on the platform at Dartford railway station in 1961, where Richards notices Chuck Berry's One Dozen Berries album under Jagger's arm. Initially, they were teamed with bass player Dick Taylor (later of the Pretty Things) and before long their ranks extended to include Jones, Stewart and occasional drummer Tony Chapman. Jones had left his home town of Cheltenham and moved to London, United Kingdom. He met Mick and Keith in a Soho pub, by this time they were occasionally sitting in with Alexis Korner's Blues Incorporated, whose drummer was Charlie Watts. Jones named the band after a Muddy Waters song entitled 'Rollin' Stone Blues' at a time when a two-word name was unusual. Korner arranged their debut gig at London's Marquee club on 21 July 1962. In their first few months the group met some opposition from jazz and blues aficionados for their alleged lack of musical 'purity' and the line-up remained unsettled for several months. In late 1962 bass player Bill Wyman (b. William Perks, 1936) replaced Dick Taylor who briefly returned to schooling, while drummers came and went including Carlo Little (from Screaming Lord Sutch's Savages) and Mick Avory (later of the Kinks, who was billed as appearing at their debut gig, but didn't play). It was not until as late as January 1963 that drummer Charlie Watts (b. 1941) reluctantly surrendered his day job and committed himself to the group. Early years After securing an eight month residency at Giorgio Gomelsky's Crawdaddy Club in Richmond, the Stones' live reputation spread rapidly through London's hip cognoscenti. One evening, the flamboyant Andrew Loog Oldham (b. 1944), appeared at the club and was so entranced by the commercial prospects of Jagger's group that he wrested them away from Gomelsky and, backed by the financial and business clout of agent Eric Easton, became their manager. Within weeks, Oldham had produced their first couple of official recordings at IBC Studios. By this time, record company scouts for Decca Records' Dick Rowe, tipped off by George Harrison, successfully signed the group. After re-purchasing the IBC demos, Oldham selected Chuck Berry's 'Come On' as their debut. The record was promoted on the prestigious UK television pop programme Thank Your Lucky Stars and the Stones were featured sporting matching hounds-tooth jackets with velvet collars. This was to be one of Oldham's few concessions to propriety for he would soon be pushing the boys image as unregenerate rebels. Unfortunately, pianist Ian Stewart was not deemed sufficiently pop star-like for Oldham's purpose and was unceremoniously removed from the line-up, although he remained road manager and occasional pianist. After supporting the Everly Brothers, Little Richard, Gene Vincent and Bo Diddley on a Don Arden UK package tour, the Stones released their second single, a gift from John Lennon and Paul McCartney entitled 'I Wanna Be Your Man'. The disc fared better than its predecessor climbing into the Top 10 in January 1964. That same month the group enjoyed their first bill-topping tour supported by the Ronettes. The early months of 1964 saw the Stones catapulted to fame amid outrage and controversy about the surliness of their demeanour and the length of their hair. This was still a world in which the older members of the community were barely coming to terms with the Beatles neatly-groomed mop tops. While newspapers asked 'Would you let your daughter marry a Rolling Stone?', the quintet engaged in a flurry of recording activity which saw the release of an EP and an album both titled The Rolling Stones. The discs consisted almost exclusively of extraneous material and captured the group at their most derivative stage. Already, however, there were strong signs of an ability to combine different styles. The third single, 'Not Fade Away', saw them fuse Buddy Holly's basic original with a chunky Bo Diddley beat that highlighted Jagger's vocal to considerable effect. The presence of Phil Spector and Gene Pitney at these sessions underlined how hip the Stones had already become in the music business after such a short time. With the momentum increasing by the month, Oldham over-reached himself by organizing a US tour which proved premature and disappointingly received. After returning to the UK, the Stones released a decisive cover of the Valentinos' 'It's All Over Now', which gave them their first number 1. A best-selling EP, Five by Five, cemented their growing reputation, while a national tour escalated into a series of near riots with scenes of hysteria wherever they played. There was an attraction to the Stones' scruffy appeal which easily translated into violence. At the Winter Gardens Blackpool the group hosted the most astonishing rock riot yet witnessed on British soil. Frenzied fans displayed their feelings for the group by smashing chandeliers and demolishing a Steinway grand piano. By the end of the evening over 50 people were escorted to hospital for treatment. Other concerts were terminated within minutes of the group appearing on-stage and the hysteria continued throughout Europe. A return to the US saw them disrupt the stagey Ed Sullivan Show prompting the presenter to ban rock 'n' roll groups in temporary retaliation. In spite of all the chaos at home and abroad, America remained resistant to their appeal, although that situation would change dramatically in the New Year. In November 1964, 'Little Red Rooster' was released and entered the New Musical Express chart at number 1, a feat more usually associated with the Beatles and, previously, Elvis Presley. The Stones now had a substantial fan base and their records were becoming more accomplished and ambitious with each successive release. Jagger's accentuated phrasing and posturing stage persona made 'Little Red Rooster' sound surprisingly fresh while Brian Jones' use of slide guitar was imperative to the single's success. Up until this point, the group had recorded cover versions as a-sides, but manager Andrew Oldham was determined that they should emulate the example of Lennon/McCartney and locked them in a room until they emerged with satisfactory material. Their early efforts, 'It Should Have Been You' and 'Will You Be My Lover Tonight?' (both recorded by the late George Bean) were bland, but Gene Pitney scored a hit with the emphatic 'That Girl Belongs to Yesterday' and Jagger's girlfriend Marianne Faithfull became a teenage recording star with the moving 'As Tears Go By'. '(I Can't Get No) Satisfaction' 1965 proved the year of the international breakthrough and three extraordinary self-penned number 1 singles. 'The Last Time' saw them emerge with their own distinctive rhythmic style and underlined an ability to fuse R&B and pop in an enticing fashion. America finally succumbed to their spell with '(I Can't Get No) Satisfaction', a quintessential pop lyric. Released in the UK during the 'summer of protest songs', the single encapsulated the restless weariness of a group already old before its time. The distinctive riff, which Keith Richard invented with almost casual dismissal, became one of the most famous hook lines in the entire glossary of pop and was picked up and imitated by a generation of garage groups thereafter. The 1965 trilogy of hits was completed with the engagingly surreal 'Get Off of My Cloud' in which Jagger's surly persona seemed at its most pronounced to date. As well as the number 1 hits of 1965, there was also a celebrated live EP, Got Live If You Want It which reached the Top 10 and, The Rolling Stones No. 2 that continued the innovative idea of not including the group's name on the front of the sleeve. There was also some well documented controversy when Jagger, Jones and Wyman were arrested and charged with urinating on the wall of an East London petrol station. Such scandalous behaviour merely reinforced the public's already ingrained view of the Stones as juvenile degenerates. With American Allen Klein replacing Eric Easton as Oldham's co-manager, the Stones consolidated their success by renegotiating their Decca contract. Their single output in the US simultaneously increased with the release of a couple of tracks unavailable in single form in the UK. The sardonic put-down of suburban Valium abuse, 'Mother's Little Helper' and the Elizabethan-styled 'Lady Jane', complete with atmospheric dulcimer, displayed their contrasting styles to considerable effect. Both these songs were included on their fourth album, Aftermath, with sessions demo'd with guitarist Jimmy Page. A breakthrough work in a crucial year, the recording revealed the Stones as accomplished rockers and balladeers, while their writing potential was emphasized by Chris Farlowe's chart-topping cover of 'Out of Time'. There were also signs of the Stones' inveterate misogyny particularly on 'Under My Thumb' and an acerbic 'Stupid Girl'. Back in the singles chart, the group's triumphant run continued with the startlingly chaotic '19th Nervous Breakdown' in which frustration, impatience and chauvinism were brilliantly mixed with scale-sliding descending guitar lines. 'Paint It Black' was even stronger, a raga-influenced piece with a lyric doom-laden and defeatist in its imagery. The Stones' nihilism reached its peak on the extraordinary 'Have You Seen Your Mother Baby, Standing in the Shadow?', a scabrous-sounding solicitation taken at breathtaking pace with Jagger spitting out a diatribe of barely coherent abuse. It was probably the group's most adventurous production to date, but its acerbic sound, lengthy title and obscure theme contributed to rob the song of sufficient commercial potential to continue the chart-topping run. Ever outrageous, the group promoted the record with a photo session in which they appeared in drag, thereby adding a clever, sexual ambivalence to their already iconoclastic public image. Drug troubles 1967 saw the Stones' anti-climactic escapades confront an establishment crackdown. The year began with an accomplished double a-sided single, 'Let's Spend the Night Together'/'Ruby Tuesday' which, like the Beatles' 'Penny Lane'/'Strawberry Fields Forever', narrowly failed to reach number 1 in the UK. The accompanying album, Between the Buttons, trod water and also represented Oldham's final production. Increasingly alienated by the Stones' bohemianism, he would move further away from them in the ensuing months and surrender the management reins to his partner Klein later in the year. On 12 February, Jagger and Richard were arrested at the latter's West Wittering home 'Redlands' and charged with drugs offences. Three months later, increasingly unstable Brian Jones was raided and charged with similar offences. The Jagger/Richard trial in June was a cause célèbre which culminated in the notorious duo receiving heavy fines and a salutary prison sentence. Judicial outrage was tempered by public clemency, most effectively voiced by the editor of The Times, William Rees-Mogg, who, borrowing a phrase from Pope, offered an eloquent plea in their defence under the leader title, 'Who Breaks a Butterfly on a Wheel?' The sentences were duly quashed on appeal in July, with Jagger receiving a conditional discharge for possession of amphetamines. Three months later, Brian Jones tasted judicial wrath with a nine-month sentence and suffered a nervous breakdown before seeing his imprisonment rescinded at the end of the year. The flurry of drug busts, court cases, appeals and constant media attention had a marked effect on the Stones' recording career which was severely curtailed. During their summer of impending imprisonment, they released the fey 'We Love You', complete with slamming prison cell doors in the background. The image of the cultural anarchists cowering in defeat was not particularly palatable to their fans and even with all the publicity, the single barely scraped into the Top 10. The eventful year ended with the Stones' apparent answer to Sgt. Pepper's Lonely Hearts Club Band - the extravagantly-titled Their Satanic Majesties Request. Beneath the exotic 3-D cover was an album of psychedelic/cosmic experimentation bereft of the R&B grit that had previously been synonymous with the Stones' sound. It featured arrangements and contributions by John Paul Jones. Although the album had some strong moments, it had the same inexplicably placid inertia of 'We Love You', minus notable melodies or a convincing direction. The overall impression conveyed to critics was that in trying to compete with the Beatles' experimentation, the Stones had somehow lost the plot. Their drug use had channelled them into laudable experimentation but simultaneously left them open to accusations of having 'gone soft'. The revitalization of the Stones was demonstrated in the early summer of 1968 with 'Jumping Jack Flash', a single that rivalled the best of their previous output. The succeeding album, Beggars Banquet, produced by Jimmy Miller, was also a return to strength and included the socio-political 'Street Fighting Man' and the brilliantly macabre 'Sympathy for the Devil', in which Jagger's seductive vocal was backed by hypnotic Afro-rhythms and dervish yelps. This song appears in a British movie by the French nouvelle vague director Jean-Luc Godard, One Plus One (1968 shown at the London Film Festival, in a version changed by the producer who put the final recording of the song at the end of the film). It mixes documentary scenes from rehearsal of Sympathy for the Devil at the Olympic Studios in London (June 1968) with scenes from a story about a white revolutionary who commits suicide when her boyfriend deserts to Black Power. While the Stones were re-establishing themselves, Brian Jones was falling deeper into drug abuse. A conviction in late 1968 prompted doubts about his availability for US tours and in the succeeding months he contributed less and less to recordings and became increasingly jealous of Jagger's leading role in the group. Richard's wooing and impregnation of Jones' girlfriend Anita Pallenberg merely increased the tension. Matters reached a crisis point in June 1969 when Jones officially left the group. The following month he was found dead in the swimming pool of the Sussex house that had once belonged to writer A. A. Milne. The official verdict was 'death by misadventure'. A free concert at London's Hyde Park two days after his death was attended by a crowd of 250,000 and became a symbolic wake for the tragic youth. Jagger released thousands of butterfly's and narrated a poem by Shelley for Jones. Three days later, Jagger's former love Marianne Faithfull attempted suicide. Mick Taylor era The group played out the last months of the 1960s with a mixture of vinyl triumph and further tragedy. The sublime 'Honky Tonk Women' kept them at number 1 for most of the summer and few would have guessed that this was to be their last UK chart topper. The new album, Let It Bleed (a parody of the Beatles' Let It Be) was an exceptional work spearheaded by 'Gimme Shelter' and revealing strong country influences ('Country Honk'), startling orchestration ('You Can't Always Get What You Want') and menacing blues ('Midnight Rambler'). It was a promising debut from John Mayall's former guitarist Mick Taylor (b. 1948) who had replaced Jones only a matter of days before his death. Even while Let It Bleed was heading for the top of the album charts, however, the Stones were singing out the 1960s to the backdrop of a Hells Angels' killing of an armed audience member at the Altamont Festival in California. The tragedy was captured on film in Albert and David Maysles' Gimme Shelter cinematic release the following year. After the events of 1969, it was not surprising that the group had a relatively quiet 1970. Jagger's contrasting thespian outings reached the screen in the form of Performance and Ned Kelly while Jean-Luc Godard's portrait of the group in the studio was delivered on Sympathy for the Devil (as One Plus One was called for its 1970 release in the U.S.). For a group who had once claimed to make more challenging and gripping films than the Beatles and yet combine artistic credibility with mass appeal, it all seemed a long time coming. After concluding their Decca contract with a bootleg-deterring live album, Get Yer Ya-Ya's Out!, the Stones established their own self-titled label, Rolling Stone Records. The first release was a three track single, 'Brown Sugar'/'Bitch'/'Let It Rock', which contained some of their best work, but narrowly failed to reach number 1 in the UK. The lead track contained a quintessential Stones riff: insistent, undemonstrative and stunning, with the emphatic brass work of Bobby Keyes embellishing Jagger's vocal power. The new album, Sticky Fingers was as consistent as it was accomplished, encompassing the bluesy 'You Gotta Move', the thrilling 'Moonlight Mile', the wistful 'Wild Horses' and the chilling 'Sister Morphine', one the most despairing drug songs ever written. The entire album was permeated by images of sex and death, yet the tone of the work was neither self-indulgent nor maudlin. The group's playful fascination with sex was further demonstrated on the elaborately designed Andy Warhol sleeve which featured a waist-view shot of a figure clad in denim, with a real zip fastener which opened to display the lips and tongue motif that was shortly to become their corporate image. Within a year of Sticky Fingers, the group returned with a double album, Exile on Main St. With Richards firmly in control, the group were rocking-out on a series of quick-fire songs. The album was severely criticized at the time of its release for its uneven quality but was subsequently re-evaluated favourably, particularly in contrast to their later work. Enter Ron Wood The Stones' soporific slide into the 1970s mainstream probably began during 1973 when their jet-setting was threatening to upstage their musical endeavours. Jagger's marriage and Richard's confrontations with the law took centre stage while increasingly average albums came and went. Goats Head Soup was decidedly patchy but offered some strong moments and brought a deserved US number 1 with the imploring 'Angie'. 1974's 'It's Only Rock 'n' Roll' proved a better song title than a single, while the undistinguished album of the same name saw the group reverting to Tamla/Motown Records for the Temptations' 'Ain't Too Proud to Beg'. The departure of Mick Taylor at the end of 1974 was followed by a protracted period in which the group sought a suitable replacement, which included secret auditions with Ry Cooder and Jimmy Page. By the time of their next release, Black and Blue, former Faces guitarist Ron Wood (b. 1947) was confirmed as Taylor's successor. The album showed the group seeking a possible new direction playing variants on white reggae, but the end results were less than impressive. By the second half of the 1970s the gaps in the Stones' recording and touring schedules were becoming wider. The days when they specially recorded for the singles market were long past and considerable impetus had been lost. Even big rallying points, such as the celebrated concert at Knebworth in 1976, lacked a major album to promote the show and served mainly as a greatest hits package. By 1977, the British music press had taken new wave to its heart and the Stones were dismissed as champagne-swilling old men, who had completely lost touch with their audience. Against the odds, the Stones responded to the challenge of their younger critics with a comeback album of remarkable power. Some Girls was their most consistent work in years, with some exceptional high-energy workouts, not least the breathtaking 'Shattered'. The disco groove of 'Miss You' brought them another US number 1 and showed that they could invigorate their repertoire with new ideas that worked. Jagger's wonderful pastiche of an American preacher on the mock country 'Far Away Eyes' was another unexpected highlight. There was even an attendant controversy thanks to some multi-racist chauvinism on the title track, not to mention 'When the Whip Comes Down' and 'Beast of Burden'. Even the cover jacket had to be re-shot because it featured unauthorized photos of the famous, most notably actresses Lucille Ball, Farrah Fawcett and Raquel Welch. To conclude a remarkable year, Keith Richard escaped what seemed an almost certain jail sentence in Toronto, Ontario for drugs offences and was merely fined and ordered to play a couple of charity concerts. As if in celebration of his release and reconciliation with his father, he reverted to his original family name Richards. The 1980s In the wake of Richards' reformation and Jagger's much-publicized and extremely expensive divorce from his model wife Bianca, the Stones reconvened in 1980 for Emotional Rescue, a rather lightweight album dominated by Jagger's falsetto and over-use of disco rhythms. Nevertheless, the album gave the Stones their first UK number 1 since 1973 and the title track was a Top 10 hit on both sides of the Atlantic. Early the following year a major US tour (highlights of which were included on Still Life) garnered enthusiastic reviews, while a host of repackaged albums reinforced the group's legacy. 1981's Tattoo You was essentially a crop of old out-takes but the material was anything but stale. On the contrary, the album was surprisingly strong and the concomitant single 'Start Me Up' was a reminder of the Stones at their 1960s best, a time when they were capable of producing classic singles at will. One of the Stones' cleverest devices throughout the 1980s was their ability to compensate for average work by occasional flashes of excellence. The workmanlike Undercover, for example, not only boasted a brilliantly menacing title track ('Undercover of the Night') but one of the best promotional videos of the period. While critics continually questioned the group's relevance, the Stones were still releasing worthwhile work, albeit in smaller doses. A three-year silence on record was broken by Dirty Work in 1986, which saw the Stones sign to CBS Records and team up with producer Steve Lillywhite, with guest contributions from Jimmy Page. Surprisingly, it was not a Stones original that produced the expected offshoot single hit, but a cover of Bob and Earl's 'Harlem Shuffle'. A major record label signing often coincides with a flurry of new work, but the Stones were clearly moving away from each other creatively and concentrating more and more on individual projects. Wyman had already tasted some chart success in 1983 with the biggest solo success from a Stones' number, 'Je Suis Un Rock Star' and it came as little surprise when Jagger issued his own solo album, She's the Boss, in 1985. A much publicized-feud with Richards led to speculation that the Rolling Stones story had come to an anti-climactic end, a view reinforced by the appearance of a second Jagger album, Primitive Cool, in 1987. When Richards himself released the first solo work of his career in 1988, the Stones' obituary had virtually been written. As if to confound the obituarists, however, the Stones reconvened in 1989 and announced that they would be working on a new album and commencing a world tour. Later that year the hastily-recorded Steel Wheels appeared and the critical reception was generally good. 'Mixed Emotions' and 'Rock and a Hard Place' were radio hits while 'Continental Drift' included contributions from the master musicians of Joujouka, previously immortalized on vinyl by the late Brian Jones. Latter years After nearly 30 years in existence, the Rolling Stones began the 1990s with the biggest grossing international tour of all time, and ended speculation about their future by reiterating their intention of playing on indefinitely. Wyman officially resigned in 1993, however. Voodoo Lounge sounded both lyrically daring and musically fresh. Riding a crest after an extraordinarily active 1995 Stripped was a dynamic semi-plugged album. Fresh sounding and energetic acoustic versions of 'Street Fighting Man', 'Wild Horses' and 'Let It Bleed' among others, emphasized just how accomplished the Jagger/Richards songwriting team had become. The year was marred however by some outspoken comments by Keith Richards on R.E.M. and Nirvana. These clumsy comments did not endear him to a younger audience, which was all the more surprising as the Stones had appeared to be in touch with contemporary rock music. Citing R.E.M. as 'wimpy cult stuff' and Kurt Cobain as 'some prissy little spoiled kid' were, at best, ill-chosen words. Bridges to Babylon was a particularly fresh-sounding album, with Charlie Watts anchoring the band's sound like never before. Their next album titled A Bigger Bang was released in 2005. This was the bands second album released in the new millennium, the first being Live Licks that was released a year earlier and featured recent Stone hits live. A Bigger Bang contained the songs 'Rain Fall Down', 'Dangerous Beauty' and 'Look What the Cat Dragged In' and other songs like 'Sweet Neo Con', 'Oh No, Not You Again' and 'Driving Too Fast'. The band's latest album is titled Shine a Light, available as a deluxe 2-disc set. This album is the soundtrack for the documentary of the same name. Tracks featured include 'Shine a Light', 'Jumpin' Jack Flash', 'Paint It Black', '(I Can’t Get No) Satisfaction', 'Sympathy for the Devil' and an intro by Martin Scorsese. This album also features the Stones with other artists such as Buddy Guy, Jack White III and Christina Aguilera. In 2008 they commenced a break from touring. In 2012 they released the greatest hit compilation Grrr!, which featured two new tracks 'Doom and Gloom' and 'One More Shot', recorded in France. Notes  (Read more...) Daniel Mietchen 1 Current Winner (to be selected and implemented by an Administrator) To change, click edit and follow the instructions, or see documentation at {{Featured Article}}. The metadata subpage is missing. You can start it via filling in this form or by following the instructions that come up after clicking on the [show] link to the right. Do you see this on PREVIEW? then SAVE! before following a link. To find out more about the use of metadata for the management of Citizendium pages, see CZ:Metadata. You may see this box for one of two reasons. Either: A - New page has been created, or subpages template was added to an existing page B - Cluster move is in progress Click either the A or B link for further instructions. [Feel free to recommend improvements to the text or links in this template] A - For a New Cluster use the following directions Subpages format requires a metadata page. Using the following instructions will complete the process of creating this article's subpages. Click the blue "metadata template" link below to create the page. On the edit page that appears paste in the article's title across from "pagename =". You might also fill out the checklist part of the form. Ignore the rest. For background, see Using the Subpages template Don't worry--you'll get the hang of it right away. Remember to hit Save! the "metadata template". However, you can create articles without subpages. Just delete the {{subpages}} template from the top of this page and this prompt will disappear. :) Don't feel obligated to use subpages, it's more important that you write sentences, which you can always do without writing fancy code. [Feel free to recommend improvements to the text or links in this template] B - For a Cluster Move use the following directions The metadata template should be moved to the new name as the first step. Please revert this move and start by using the Move Cluster link at the top left of the talk page. The name prior to this move can be found at the following link. [Feel free to recommend improvements to the text or links in this template] PD Image Figure 1. Euler angles. From left to right: initial configuration, after rotation over angle α, after rotation over angle β, and after rotation over angle γ. In physics, mathematics, and engineering, Euler angles are three rotation angles, often denoted by 0 ≤ α ≤ 2π, 0 ≤ β ≤ π, and 0 ≤ γ ≤ 2π, although the notation φ, θ, ψ is also common. Any rotation of a 3-dimensional object can be performed by three consecutive rotations over the three Euler angles. Different conventions are in use: a rotation can be active (the object is rotated, the system of axes is fixed in space), or passive (the object is fixed in space, the axes are rotated). Also the choice of rotation axes may vary; an active convention common in quantum mechanical applications is the z-y′-z′ convention. Attach a system of Cartesian coordinate axes to the body that is to be rotated (the coordinate frame is fixed to the body and is rotated simultaneously with it); in the figure the body-fixed frame is shown in red and labeled by lowercase letters. First rotate around z, then around the new body-fixed y-axis, y′, and finally around z′. Another convention often used is the z-x′-z′ convention, where instead of over the new y-axis the second rotation is over the new x-axis. Also the z-y-x convention is used (and will be discussed below). The right-hand screw rule is practically always followed: the rotation axis is a directed line and a positive rotation is as a cork screw driven into the positive direction of the axis. In older literature left-handed Cartesian coordinate frames appear sometimes, but in modern literature right-handed frames are used exclusively. Euler angles are used in many different branches of physics and engineering. The present article is written from the point of view of molecular physics, where the objects to be rotated are molecules and applications are often of quantum mechanical nature. The angles are named after the 18th century mathematician Leonhard Euler who introduced in 1765 two of the three for an axially symmetric body where the third angle, γ, does not play a role. Geometric discussion In Figure 1 the space-fixed (laboratory) axes are labeled by capital X, Y, and Z and are shown in black. The body to be rotated is not shown, but a system of axes fixed to it is shown in red. One may use any convenient orthonormal frame as a body-fixed frame. Often the body-fixed axes are principal axes, that means that they are eigenvectors of the inertia tensor of the body. Also symmetry axes, when present, may be used. When the body has symmetry axes, the principal axes often coincide with these. PD Image Figure 2. Rotation of r to r′. On the left around z-axis over α (φ increases), on the right around y-axis over β (φ decreases). Both rotation axes point toward the reader. The z-y′-z′ convention will be followed. Initially, the two frames coincide, and the path to a final arbitrary orientation of the body—and its frame—is depicted on Figure 1. The first rotation is around the z-axis, which coincides with the Z-axis. The x- and y-axis move in a plane perpendicular to the z-axis over an angle α. The second rotation is in a plane through the origin perpendicular to the y′-axis. The angle is β. The present convention has the practical advantage that the z′-axis has the usual spherical polar coordinates α ≡ φ (longitude angle) and β ≡ θ (colatitude angle) with respect to the space-fixed frame. The final rotation is in a plane perpendicular to the z′-axis over an angle γ. From geometric considerations follows that any orientation of the body-fixed frame in space may be obtained. Write $\mathbf {R} (\varphi ,{\hat {n}})$ for the rotation matrix that describes a rotation around the unit vector ${\hat {n}}$ over an angle $\varphi$. Clearly the three consecutive Euler rotations correspond to rotations around the unit vectors along the body-fixed axes z, y′, and z′ over angles α β, and γ, respectively. Because a matrix acts on a column vector to its right, the order in the matrix product is as in the leftmost term in the following equation. It will be shown that the corresponding matrix product can be written in reverse order (but around fixed, unprimed, axes z, y, z), that is, ${\begin{aligned}\mathbf {R} (\gamma ,{\hat {e}}_{z'})\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\alpha ,{\hat {e}}_{z})&=\mathbf {R} (\alpha ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y})\mathbf {R} (\gamma ,{\hat {e}}_{z})\\&={\begin{pmatrix}\cos \alpha &-\sin \alpha &0\\\sin \alpha &\cos \alpha &0\\0&0&1\\\end{pmatrix}}{\begin{pmatrix}\cos \beta &0&\sin \beta \\0&1&0\\-\sin \beta &0&\cos \beta \\\end{pmatrix}}{\begin{pmatrix}\cos \gamma &-\sin \gamma &0\\\sin \gamma &\cos \gamma &0\\0&0&1\\\end{pmatrix}}\\&={\begin{pmatrix}\cos \alpha \cos \beta \cos \gamma -\sin \alpha \cos \gamma \;&\;-\cos \alpha \cos \beta \sin \gamma -\sin \alpha \cos \gamma \;&\;\cos \alpha \sin \beta \\\sin \alpha \cos \beta \cos \gamma +\cos \alpha \sin \gamma \;&\;-\sin \alpha \cos \beta \sin \gamma +\cos \alpha \cos \gamma \;&\;\sin \alpha \sin \beta \\-\sin \beta \cos \gamma \;&\;\sin \beta \sin \gamma \;&\;\cos \beta \end{pmatrix}}\end{aligned}}$ Note that the third column contains the Cartesian coordinates with respect to the space-fixed frame of ${\hat {e}}_{z''}$ expressed in sines and cosines of spherical polar angles. The first and second column contain by definition expressions for the Cartesian coordinates of ${\hat {e}}_{x'''}$ and ${\hat {e}}_{y''}$, respectively, but evidently these are not solely in terms of spherical polar angles, γ also enters. Before proving the first equality in the above equation (reversal of order), we derive the matrix for a rotation around the z-axis, see the left drawing in Figure 2. The rotated vector has components ${\begin{pmatrix}\cos(\alpha +\phi )\\\sin(\alpha +\phi )\\0\end{pmatrix}}={\begin{pmatrix}\cos \alpha \cos \phi -\sin \alpha \sin \phi \\\sin \alpha \cos \phi +\cos \alpha \sin \phi \\0\end{pmatrix}}={\begin{pmatrix}\cos \alpha &-\sin \alpha &0\\\sin \alpha &\cos \alpha &0\\0&0&1\\\end{pmatrix}}{\begin{pmatrix}\cos \phi \\\sin \phi \\0\\\end{pmatrix}}\equiv \mathbf {R} (\alpha ,{\hat {e}}_{z}){\begin{pmatrix}\cos \phi \\\sin \phi \\0\end{pmatrix}}.$ We used here the relations well-known from trigonometry for the sine and cosine of a sum angle. The derivation of the matrix for a rotation around the y-axis proceeds along the same lines. Note, however, that the angle of a vector with the x-axis decreases by a rotation around the positive y-axis (see right-hand drawing in Figure 2). To prove the first equality (reversal of the order in the angles), a property of rotation matrices is used. A rotation (orthogonal 3×3) matrix A, transforming a rotation axis, gives rise to the following similarity equation, $\mathbf {R} (\varphi ,\mathbf {A} {\hat {n}})=\mathbf {A} \mathbf {R} (\varphi ,{\hat {n}})\mathbf {A} ^{\mathrm {T} },$ where the superscript T indicates the transpose of the matrix. For rotation matrices the transposed matrix is equal to the inverse of the matrix. From this similarity relation follows that $\mathbf {R} (\gamma ,{\hat {e}}_{z'})=\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y'})^{\mathrm {T} },$ so that $\mathbf {R} (\gamma ,{\hat {e}}_{z'})\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y'})^{\mathrm {T} }\;\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\alpha ,{\hat {e}}_{z}).$ Also $\mathbf {R} (\beta ,{\hat {e}}_{y'})=\mathbf {R} (\alpha ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y})\mathbf {R} (\alpha ,{\hat {e}}_{z})^{\mathrm {T} },$ so that $\mathbf {R} (\beta ,{\hat {e}}_{y'})\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\alpha ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y})\mathbf {R} (\alpha ,{\hat {e}}_{z})^{\mathrm {T} }\;\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\alpha ,{\hat {e}}_{z})\mathbf {R} (\beta ,{\hat {e}}_{y})\mathbf {R} (\gamma ,{\hat {e}}_{z}),$ where it is used that rotations around the same axis commute, that is, $\mathbf {R} (\alpha ,{\hat {e}}_{z})^{\mathrm {T} }\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\gamma ,{\hat {e}}_{z})\mathbf {R} (\alpha ,{\hat {e}}_{z})^{\mathrm {T} }\mathbf {R} (\alpha ,{\hat {e}}_{z})=\mathbf {R} (\gamma ,{\hat {e}}_{z})$ and the required result is proved. Algebraic treatment In the proof that any rotation can be written as three consecutive rotations, an appeal was made to the geometric insight of the reader. The same result can be proved more rigorously by algebraic means. To that end the notation is somewhat shortened: $\mathbf {R} _{z}(\omega )\equiv \mathbf {R} (\omega ,{\hat {e}}_{z})\quad {\hbox{and}}\quad \mathbf {R} _{y}(\omega )\equiv \mathbf {R} (\omega ,{\hat {e}}_{y}).$ Theorem A proper rotation matrix R can be factorized thus $\mathbf {R} =\mathbf {R} _{z}(\omega _{3})\;\mathbf {R} _{y}(\omega _{2})\;\mathbf {R} _{x}(\omega _{1})$ which is referred to as the Euler z-y-x parametrization, or also as $\mathbf {R} =\mathbf {R} _{z}(\alpha )\;\mathbf {R} _{y}(\beta )\;\mathbf {R} _{z}(\gamma )\quad$ the Euler z-y-z parametrization. Proof First the Euler z-y-x-parametrization will be proved by an algorithm for the factorization of a given matrix R ≡ (r1, r2, r3). Second the z-y-z parametrization will be proved; this parametrization is—as shown above—equivalent to the z′-y′-z parametrization with angles in reverse order. :A Fortran subroutine based on the algorithm is given on the code page. To prove the z-y-x parametrization we consider the matrix product $\mathbf {R} _{z}(\omega _{3})\,\mathbf {R} _{y}(\omega _{2})={\begin{pmatrix}\cos \omega _{3}\cos \omega _{2}&-\sin \omega _{3}&\cos \omega _{3}\sin \omega _{2}\\\sin \omega _{3}\cos \omega _{2}&\cos \omega _{3}&\sin \omega _{3}\sin \omega _{2}\\-\sin \omega _{2}&0&\cos \omega _{2}\\\end{pmatrix}}\equiv (\mathbf {a} _{1},\mathbf {a} _{2},\mathbf {a} _{3}).$ The columns of the matrix product are for ease of reference designated by a1, a2, and a3. Note that the multiplication by $\mathbf {R} _{x}(\omega _{1})\equiv {\begin{pmatrix}1&0&0\\0&\cos \omega _{1}&-\sin \omega _{1}\\0&\sin \omega _{1}&\cos \omega _{1}\end{pmatrix}}$ on the right does not affect the first column, so that a1 = r1 (the first column of R). Solve $\omega _{2}\;$ and $\omega _{3}\;$ from the first column of R (which is known), $\mathbf {a} _{1}={\begin{pmatrix}\cos \omega _{3}\;\cos \omega _{2}\\\sin \omega _{3}\;\cos \omega _{2}\\-\sin \omega _{2}\\\end{pmatrix}}={\begin{pmatrix}R_{11}\\R_{21}\\R_{31}\\\end{pmatrix}}\equiv \mathbf {r} _{1}.$ This is possible. First solve $\omega _{2}\;$ for $-\pi /2\leq \omega _{2}\leq \pi /2$ from $\sin \omega _{2}=-R_{31}.\,$ Then solve $\omega _{3}\;$ for $0\leq \omega _{3}\leq 2\pi$ from the two equations: $\cos \omega _{3}={R_{11} \over \cos \omega _{2}},\qquad \sin \omega _{3}={R_{21} \over \cos \omega _{2}}.$ The angles $\omega _{2}\;$ and $\omega _{3}\;$ determine fully the vectors a2 and a3. Since a1, a2 and a3 are the columns of a proper rotation matrix they form an orthonormal right-handed system. The plane spanned by a2 and a3 is orthogonal to $\mathbf {a} _{1}\equiv \mathbf {r} _{1}$ and hence the plane contains $\mathbf {r} _{2}$ and $\mathbf {r} _{3}$. Thus the latter two vectors are a linear combination of the first two, $(\mathbf {r} _{2},\mathbf {r} _{3})=(\mathbf {a} _{2},\mathbf {a} _{3}){\begin{pmatrix}\cos \omega _{1}&-\sin \omega _{1}\\\sin \omega _{1}&\cos \omega _{1}\\\end{pmatrix}}.$ Since $\mathbf {r} _{2},\;\mathbf {a} _{2},\;\mathbf {a} _{3}$ are known orthonormal vectors, we can compute ${\begin{aligned}\mathbf {a} _{2}\cdot \mathbf {r} _{2}=&\cos \omega _{1}\\\mathbf {a} _{3}\cdot \mathbf {r} _{2}=&\sin \omega _{1}.\end{aligned}}$ These equations give $\omega _{1}\;$ with $0\leq \omega _{1}\leq 2\pi$. The angle ω1 gives the matrix $\mathbf {R} _{x}(\omega _{1})$ with ${\begin{aligned}\mathbf {R} \equiv (\mathbf {r} _{1},\mathbf {r} _{2},\mathbf {r} _{3})=(\mathbf {r} _{1},\mathbf {a} _{2},\mathbf {a} _{3})\mathbf {R} _{x}(\omega _{1})=(\mathbf {a} _{1},\mathbf {a} _{2},\mathbf {a} _{3})\mathbf {R} _{x}(\omega _{1})=\mathbf {R} _{z}(\omega _{3})\,\mathbf {R} _{y}(\omega _{2})\,\mathbf {R} _{x}(\omega _{1}).\end{aligned}}$ This gives the required z-y-x factorization of the arbitrary proper orthogonal matrix R. The proof of the Euler z-y-z parametrization is obtained by a small modification of the previous proof. We start by retrieving the spherical polar coordinates $\omega _{2}\;$ and $\omega _{3}\;$ of the unit vector $\mathbf {r} _{3}=\mathbf {a} _{3}$, the third column [the rightmost multiplication by Rz(ω1) does not affect r3]. Then consider $(\mathbf {r} _{1},\;\mathbf {r} _{2})=(\mathbf {a} _{1},\;\mathbf {a} _{2}){\begin{pmatrix}\cos \omega _{1}&-\sin \omega _{1}\\\sin \omega _{1}&\cos \omega _{1}\\\end{pmatrix}}$ or, $\mathbf {a} _{1}\cdot \mathbf {r} _{1}=\cos \omega _{1}\;,\quad \mathbf {a} _{2}\cdot \mathbf {r} _{1}=\sin \omega _{1}.$ The equation for R can be written as $(\mathbf {r} _{1},\mathbf {r} _{2},\mathbf {r} _{3})=(\mathbf {a} _{1},\mathbf {a} _{2},\mathbf {r} _{3})\,\mathbf {R} _{z}(\omega _{1})=\mathbf {R} _{z}(\omega _{3})\,\mathbf {R} _{y}(\omega _{2})\,\mathbf {R} _{z}(\omega _{1})\;,$ which proves the Euler z-y-z parametrization. Clearly, this factorization is equal to the one given in the previous section, with $\omega _{3}\equiv \alpha ,\quad \omega _{2}\equiv \beta ,\quad \omega _{1}\equiv \gamma .$ Note (Read more...) 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