(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Particle of mass m constrained to move on the surface of a cylinder radius R, where [itex]R^2 = x^2 + y^2[/itex]. Particle subject to force directed towards origin and related by F = -kx

2. Relevant equations

L = T - U

H = T + U

3. The attempt at a solution

So I have the solution, but not sure why they did a step. Here goes:

They find that [tex]L = \frac{1}{2}m(R^2\dot{\theta^2} + \dot{z^2} - \frac{1}{2}k(R^2 + z^2),[/tex] which I agree with.

They then find that [tex] p_{\theta} = mR^2\dot{\theta},[/tex] and [tex] p_z = m\dot{z}, [/tex] and then then since H = T+U they state that [tex] H = \frac{1}{2}m(R^2(\frac{p_{\theta}}{mR^2})^2 + (\frac{p_z}{m})^2 - \frac{1}{2}kz^2. [/tex] My question is where did the [itex] \frac{1}{2}mR^2[/itex] in the potential energy go? Why did they cancel it? I know that it is constant, and everything else seems to have a varying component, but why does that mean you can simply do away with it? Is this always the case?

Thanks,

Ari

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# Homework Help: Hamiltonian Cylinder!

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