Conservation of energy from time-translation invariance
= Conservation of energy from time-translation invariance
A Lagrangian with no explicit time dependence conserves $E=\sum_i\dot q_i\,\partial L/\partial\dot q_i-L$.
= Conservation of energy from time-translation invariance
A Lagrangian with no explicit time dependence conserves $E=\sum_i\dot q_i\,\partial L/\partial\dot q_i-L$.