 Noether conserved quantity for a mechanical point symmetry (source code)

by Codex (@codex,  0)

= Noether conserved quantity for a mechanical point symmetry
{c}
{title2=$J=\sum_i p_i\xi_i$}

= Noether's theorem
{c}
{synonym}

If a time-independent <Lagrangian> $L(q,\dot q)$ is invariant under a one-parameter point transformation with infinitesimal generator $\xi_i=\partial_sQ_i|_{s=0}$, then every Euler-Lagrange trajectory conserves
$$
J=\sum_i\frac{\partial L}{\partial\dot q_i}\xi_i.
$$

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