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Unformatted text preview: ) xyz ( Ï‰ Î¸ ) xyz = D T Ï‰ Î¸ = D T ï£« ï£¬ ï£ Â· Î¸ ï£¶ ï£· ï£¸ = ï£« ï£¬ ï£ Â· Î¸ cos Ï† Â· Î¸ sin Ï† ï£¶ ï£· ï£¸ . (6) To obtain the space frame components of Ï‰ Ïˆ we can use either A T or D T C T , since their action is the same. We get ( Ï‰ Ïˆ ) xyz = A T Ï‰ Ïˆ = D T C T ï£« ï£¬ ï£ Â· Ïˆ ï£¶ ï£· ï£¸ = ï£« ï£¬ ï£¬ ï£ Â· Ïˆ sin Î¸ sin Ï† âˆ’ Â· Ïˆ sin Î¸ cos Ï† Â· Ïˆ cos Î¸ ï£¶ ï£· ï£· ï£¸ . (7) With ( Ï‰ Ï† ) xyz = ï£« ï£¬ ï£ Â· Ï† ï£¶ ï£· ï£¸ , (8) 1 all of the intermediate results are complete, and we simply add the corresponding components of Eqs.(6), (7), and (8) to obtain ï£« ï£ Ï‰ x Ï‰ y Ï‰ z ï£¶ ï£¸ = ï£« ï£¬ ï£¬ ï£ Â· Î¸ cos Ï† + Â· Ïˆ sin Î¸ sin Ï† Â· Î¸ sin Ï† âˆ’ Â· Ïˆ sin Î¸ cos Ï† Â· Ï† + Â· Ïˆ cos Î¸ ï£¶ ï£· ï£· ï£¸ , (9) which is the desired result. 2...
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.
 Fall '10
 Wilemski
 mechanics

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