= Lagrangian energy function
{c}
{title2=$\mathcal E=\sum_i\dot q_i\partial L/\partial\dot q_i-L$}
For a <Lagrangian> $L(q,\dot q,t)$, its energy function satisfies $d\mathcal E/dt=-\partial L/\partial t$ along the <Euler-Lagrange equations>. This follows by differentiating and cancelling the $\ddot q_i\partial L/\partial\dot q_i$ terms. It is conserved when $L$ has no explicit time dependence. For imposed moving constraints it need not coincide with inertial <mechanical energy>; a <Jacobi integral> is an important example.
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