HW8_prob4_GPS20_G9 - Problem GPS 4.20 (2nd ed. 4-9) In...

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Problem GPS 4.20 (2 nd ed. 4-9) In general, we would need six generalized coordinates to describe the motion of the sphere. Three of these would be for the center of mass ( X , Y , Z )andthree for the orientation of a body f xed frame rotating with the sphere (the three Euler angles). Because the sphere is con f ned to a plane, one COM coordinate, say Z , is always a constant. So our task comes down to f nding suitable relationships among ( X , Y , ψ , θ , φ ) to govern the constraint of rolling without slipping. Let’s start by imagining that we are sitting at the origin of a space f xed Cartesian frame (SFF) watching the sphere rolling in the x y plane located at z =0 . The COM vector R runs from the origin of the SFF to the center of the sphere. Another vector r runs from the center of the sphere to its surface. This vector is f xed in the sphere, so it rotates as the sphere rolls. Finally, a third vector r 0 connects the SFF origin with the end of vector r on the sphere’s
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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.

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HW8_prob4_GPS20_G9 - Problem GPS 4.20 (2nd ed. 4-9) In...

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