Analytical Mech Homework Solutions 161

Analytical Mech Homework Solutions 161 - L = mr r L p = =...

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r L p mr r == ± ± r p r m = ± 2 L p mr θ ± ± 2 p mr = ± 2 2 2 22 t r ii r p p k Hp q L p r p e mm rr β =− = + ± ±± ± Substituting for and r ± ± 2 2 2 t r p p k He =+ (b) H = T + V … which is time-dependent (c) E is not conserved 10.29 Locate center of coordinate system at C.M. The potential is independent of the center of mass coordinates. Therefore, they are ignorable. (r 1 , θ 1 ) LTV = () 2 2 2 2 2 11 1 2 11 1 22 2 mr r r kr r l θθ = ++ + −+ where l is the length of the relaxed spring and k is the spring constant. 1 r L p mr r ± ± 1 1 1 r p r m = ± 2 1 L 1 p mr ± ± 1 1 2 p = ± (r 2 , θ 2 ) … and similarly for m 2 q L 2 12 1 2 1 2 pp Hk r mm r − + r r l Equations of motion … First, θ
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