= Conservation of mechanical energy
{title2=$T+V=\mathrm{constant}$}
For constant masses, a time-independent <potential energy> $V$ and forces $\boldsymbol F_i=-\nabla_iV+\boldsymbol R_i$ with zero total extra power $\sum_i\boldsymbol R_i\cdot\boldsymbol v_i=0$, <Newton's second law> gives $dT/dt=-dV/dt$. Thus <mechanical energy> is conserved. Smooth stationary constraint reactions and a purely magnetic <Lorentz force> supply zero power. This is more restrictive than <conservation of energy> in general, which may include thermal or other internal forms.
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