Energy function
= Energy function
For a Lagrangian $L(q,\dot q,t)$, its energy function is
$$
E=\sum_i\dot q_i\frac{\partial L}{\partial\dot q_i}-L.
$$
It is conserved along Euler-Lagrange trajectories when $L$ has no explicit time dependence.
= Energy function
For a Lagrangian $L(q,\dot q,t)$, its energy function is
$$
E=\sum_i\dot q_i\frac{\partial L}{\partial\dot q_i}-L.
$$
It is conserved along Euler-Lagrange trajectories when $L$ has no explicit time dependence.