An extremum variational principle for classical Hamiltonian systems

Abstract

A variational principle for a mechanical systems with n-degrees of freedom, which is subject to conservative generalized forces, is formulated. Necessary conditions for its extremum are given in detail. Two possibilities for constructing the functional are established. The first one is applicable if the canonical equations have certain simple algebraic properties, the second one is applicable in the general case. The theory is based on the concept of a mechanical system, but the results obtained can be applied to all problems in mathematical physics admitting Hamiltonian description. Finally, the theory is used for obtaining approximate solution of nonlinear mechanical problem with two degrees of freedom. © 1984 Springer-Verlag.