- #1
Liquidxlax
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Homework Statement
a) the lagrangian for a system of one degree of freedom can be written as.
L= (m/2) (dq/dt)2sin2(wt) +q(dq/dt)sin(2wt) +(qw)2
what is the hamiltonian? is it conserved?
b) introduce a new coordinate defined by
Q = qsin(wt)
find the lagrangian and hamiltonian with the new coordinate and is it conserved?
Homework Equations
qp-L = H
The Attempt at a Solution
Just wondering what the method is to solve b) or is it as simple as
q = Q/sin(wt)
(dq/dt) = (dQ/dt)/sin(wt) - Qwcos(wt)/(sin2(wt))
subbing that in and solving?
I'm assuming that this change of coordinate is supposed to make the Hamiltonian independent of time and therefore conserved.
Yet what i found is not conserved, so i assume i used the wrong method.