Integrability of implicit differential equations

Abstract

The problem of integrability of differential equations is discussed. Examples and integrability criteria are given. An algorithm for extracting the integrable part of an implicit differential equation is formulated. A procedure for generating a class of submanifolds of the cotangent bundle is defined. This procedure is then used for generating implicit differential equations in the phase space of a mechanical system. Integrability criteria of such equations are established and an extraction algorithm is formulated.