hw_7 - (iii) central force motion with an harmonic...

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Physics 821 Spring Quarter 2007 Dr. Herbst HOMEWORK ASSIGNMENT # 7 DUE: TUESDAY, 29 MAY 2007 Goldstein et al. Chapter 6 Exercises 5, 12, 16 Deduce Hamilton’s equations of motion for the following problems and identify any cyclic coordinates: (i) the spherical pendulum (spherical polar coordinates) (ii) the symmetric top with one point fixed in a gravitational field (Euler angles)
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Unformatted text preview: (iii) central force motion with an harmonic potential kr 2 (Cartesian coordinates) (iv) a relativistic particle of rest mass m moving along the x-axis under a potential V(x). Hint: L = m c 2 { 1 [1 ( dx/dt ) 2 / c 2 ] 1/2 } V(x)...
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