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Incoming links: Jacobi integral of a rigidly rotating potential
Past exam of the mathematics course of the University of Cambridge 2004 iii Paper 66 4 i 2 Solution Created 2026-10-03 Updated 2026-10-14
No global isolating integral is possible in a sufficiently general time-dependent system without surviving symmetries or other invariants. Foreven 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.