Answer to Question #274940 in Classical Mechanics for zaw myo

Question #274940

A particle of mass m moves under the influence of gravity along the helix z =kθ, r =constant, where k is a constant and z is vertical. Obtain the Hamiltonian equations of motion.


1
Expert's answer
2021-12-06T09:41:52-0500

z=kθ,z=k\theta,

L=TU,L=T-U,

T=kmθ22,T=\frac{km\theta^2}2,

U=kmgθ¨,U=kmg\ddot{\theta},

LθddtLθ˙=0,\frac{\partial L}{\partial \theta}-\frac d{dt}\frac{\partial L}{\partial \dot {\theta}}=0,

kmθθ˙mgθ¨=0.km\theta\dot{\theta}-mg\ddot{\theta}=0.


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