 #1
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Homework Statement
Show that if the Lagrangian does not explicitly depend on time that the Hamiltonian is a constant of motion.
Homework Equations
see below
The Attempt at a Solution
method attached here:
Apologies this is probably a bad question, but just on going from the line ##dH## to ##dH/dt## I see the##d/dt## has hit the ##dq_0## terms only, I don’t understand why a product rule hasn’t been used, so I would get:
##\frac{dH}{dt}=\sum_{u} \dot{q_u} (\frac{dp_{u}}{dt}\frac{\partial L}{\partial q_u} )+ \ddot{q_u}dp_{u}\frac{d}{dt}(\frac{\partial L}{\partial q_u}) dq_u ##
Many thanks
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