Completely and Partially Integrable Systems of Total Differential Equations

Abstract

Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) $Partiallyintegrablesystems$, where the set of equations of motion is only integrable. b) {\it Completely integrable systems}, where the set of equations of motion and the action function is integrable. Two examples are studied.

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