An always extremum variational principle for classical mechanics via a canonical transformation (Q1814294)

Motion of a mechanical system with \(n\) degrees of freedom is examined by a special canonical variables. In that phase space the authors construct a variational principle as the difference between primal and dual functionals. It is proved that the principle has a weak maximum on the exact solution of the motion equations in the new phase space. Also, the necessary conditions for global extremality of the principle are given. The possible practical applications of the variational principle are shown. It could be used for: 1) finding approximate solutions for different problems --- the Ritz method, 2) development of a version of the finite element technique. The numerical value of the functional can be used as a measure for convergence during numerical integration and for error estimate of the approximate solution.