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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