- #1

Coffee_

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- 2

For anyone using different terminology, by rheonomic (time dependent constraints) I mean that if a system has N degrees of freedom, the position vectors of each particle of the system are given by ##\vec{r}_i(q_1,q_2,...,q_n,t)##. Where ##q_i## are generalized coordinates and at least ONE of all these vectors has explicit time dependence.

Anyway with this setup there are two possible cases:

1) ##\frac{\partial L} {\partial t} = 0 ##

2) ##\frac{\partial L} {\partial t} \ne 0 ##

For 1) all I'm able to do is prove that the Hamiltonian is NOT equal to the energy and that the Hamiltonian is obviously conserved. This does not yet in general say if energy is conserved or not. I have already encountered examples where this is the case but energy is not conserved. Is there a general statement about energy one can make in these two cases for time dependent constraints?

For 2) I'm pretty sure that energy is never conserved but still note sure how to prove that.