homework2.20100126.4b5f93ff434910.15134773

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TAM 412, Homework 2, due February 3, 2010 Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] 1. Do exercise 1.7 of the textbook. 2. Do exercise 1.8 of the textbook. 3. Do exercise 1.5 of the textbook. 4. Show that when the transition matrix is expressed in terms of Euler angles, the vector v whose T components are μ (1 cos ( ψ ϕ )) tan θ 2 , sin ( ψ ϕ )tan θ 2 , cos ϕ cos ψ T has the same components in ˜ T . What can be said about the relationship between T and ˜ T in terms of v ? 5. Suppose that θ = π 4 , ϕ = π 4 ,and ψ = π 4 . (a) Compute the components of v found in 4. (b) Compute the T components of the vector e 3 × v andshowthatitisperpend icu larto v and e 3 . (c) Compute the T components of the vector ˜ e 3 × v andshowthatitisperpend icu larto v and ˜ e
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Unformatted text preview: a heading, click on the f lled triangle next to the corresponding phrase. To read a speci f c topic, click on the link. The topics discussed below can all be found under the heading ’Core Language’. Speci f cally, read about • the topic ’De f ning Functions’, which can be found under the subheading ’Functions and Programs’; • the topic ’Modules and Local Variables’, which can be found under the subheading ’Modularity and the Naming of Things’; • the topic ’Conditionals’, which can be found under the subheading ’Evaluation of Expressions’. 6. Write a Mathematica function that takes three arguments a , b , and c and returns the two roots to the quadratic polynomial p ( x ) = ax 2 + bx + c . 7. Write a Mathematica function that takes a transition matrix and returns the corresponding Euler angles. 1...
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