= Solution
\b[No global isolating integral is possible in a sufficiently general time-dependent system without surviving symmetries or other invariants.] For
$$
E=\tfrac12v^2+\Phi(\mathbf x,t),\qquad \frac{dE}{dt}=\frac{\partial\Phi}{\partial t},
$$
even energy is then not conserved, and nonsymmetric forcing can destroy all global constraints on the orbit. Time dependence alone does not imply this result: a central time-dependent force still conserves <angular momentum>, and a rigidly rotating potential can conserve a <Jacobi integral of a rigidly rotating potential>. The case of no integrals requires absence of such additional structure. A fixed point or locally defined flow labels are not the global orbit family considered here.
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