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homework4.20100210.4b73387a473b13.93424552 - f cally read...

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TAM 412, Homework 4, due February 17, 2010 Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] 1. Do exercise 2.1 of the textbook. Feel free to use the Mathematica ’VectorPlot’ and ’ContourPlot’ commands. 2. Do exercise 2.5 of the textbook. 3. Do exercise 3.2 of the textbook. 4. Do exercise 3.3 of the textbook. 5. Do exercise 3.8 of the textbook. For the next exercise, access the ’Virtual Book’ under the Mathematica ’Help’ menu. To expand 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
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Unformatted text preview: f cally, read about • the topics ’Applying Functions to Lists and Other Expressions’ and ’Applying Functions to Parts of Expressions’, which can be found under the subheading ’Functional Operations’; 6. Write a Mathematica function that f nds Lagrange’s equations in terms of a set of generalized coordi-nates when provided with the kinetic energy in terms of a di f erent set of generalized coordinates and the coordinate transformation between the two sets of generalized coordinates. 1...
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