It is shown that all classical dynamical problems involving $n$ degrees of freedom automatically possess invariances under the $O_{n+1\mathrm{}}$ and $S{U}_n$ algebras, independent of the functional form of the Hamiltonian. For spherically symmetric systems with three degrees of freedom, the existence of a vector constant of motion is established.

• Received 5 October 1966

DOI:https://doi.org/10.1103/PhysRev.155.1383