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.
z=kθ,z=k\theta,z=kθ,
L=T−U,L=T-U,L=T−U,
T=kmθ22,T=\frac{km\theta^2}2,T=2kmθ2,
U=kmgθ¨,U=kmg\ddot{\theta},U=kmgθ¨,
∂L∂θ−ddt∂L∂θ˙=0,\frac{\partial L}{\partial \theta}-\frac d{dt}\frac{\partial L}{\partial \dot {\theta}}=0,∂θ∂L−dtd∂θ˙∂L=0,
kmθθ˙−mgθ¨=0.km\theta\dot{\theta}-mg\ddot{\theta}=0.kmθθ˙−mgθ¨=0.
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