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How to find constant of motion from hamiltonian?
Given that for a one dimensional system, H(hamiltonian)=(p^2/2)-{1/(2q^2)}.
How to show that there is a constant of motion D=pq/2 - Ht ?
1 Answer
- ?Lv 79 years agoFavorite Answer
dD/dt = 1/2 p dq/dt + 1/2 q dp/dt - H,
( no dH/dt term, because H has no explicit time dependence.)
But from the equations of motion in this Hamilton formalism:
dp/dt = -dH/dq = -1/q^3
dq/dt = dH/dp = p
Upon substitution you will see dD/dt = 0, so D is conserved.
