= Solution
A <constant of motion> is a quantity preserved along the evolution, possibly with explicit time dependence. For $C(\mathbf x,\mathbf v,t)$ in a <gravitational potential> $\Phi$, the preservation condition is
$$
\boxed{\frac{dC}{dt}=\partial_tC+\mathbf v\cdot\nabla_xC-\nabla\Phi\cdot\nabla_vC=0.}
$$
For free motion, $\mathbf x-\mathbf v t$ is a useful explicitly time-dependent example. Such initial-position labels should not be counted as stationary <isolating integrals> of a galactic <orbit>.
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