Separation of classical equations of motion based on symmetry

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Abstract
We show that an invariance of a system of N particles simplifies the solution of the classical equations of motion.A transformation can be constructed in a straightforward manner to yield a set of active and redundant coordinates in which Hamilton’s equations are separable. That is, the redundant coordinates are cyclic and the kinetic energy is block diagonal between the two sets. Furthermore, the active coordinates have properties very similar to the parent Cartesian coordinates; e.g., the derivatives of the Hamiltonian remain unchanged. The numerical application of the procedure is very straightforward; we have performed trajectories of symmetric motions of an A2B-type molecule within the subspace of the C2v configurations.