Question

CAN YOU PLEASE JUST GIVE ME THE ANSWER FOR PART ( d)

2. Consider a bead of mass m sliding without friction on a wire that is bent into the shape of a parabola and spun with constant angular velocity ω about its vertical axis. Use cylindrical polar coordinates and let the equation of the parabola be : -kp (a) Find the Lagrangian in terms of p as the generalized coordinate. (b) Find the Hamiltonian for the system. (c) Is the Hamiltonian conserved? (d) From the Hamiltonian identify any equilibrium positions and analyze their stability.

Answer 1

as the last part of the question is asked, i am giving an idea to solve it. please apply this to your hamitonian equation and get the result. if you are unable to do it, please text. i am solving it by giving an example because this question has to be solved by solving all the remaining subparts which is difficult and so i adpoted this method. hope you understood.

As the last part of the question is asked, i am giving an idea to solve it. please apply this to your Hamiltonian equation and get the result. if you are unable to do it, please text. i am solving it by giving an example because this question has to be solved by solving all the remaining subparts which is difficult and so i adopted this method. hope you understood. \r\n stability is derived by using the final Hamiltonian equation. As only last part is asked, I will explain it by giving an example. Consider the following Hamiltonian. H(theta, p_theta) = p^2_theta/2 m L^2 + mgl(1 - cos theta) for this solve partial differential H/ partial differential theta and partial differential H/ partial differential p_theta p_theta = m L^2 theta we get partial differential H/ partial differential theta and partial differential H/ partial differential p_theta to be zero these both set the equilibrium (0, 0) and (pi, 0) here (0, 0) will be stable according to