Analytic representation of dynamical systems using pseudo-inverse methods

Abstract

The term `analytic representation' in configuration space is often used for the representation of a physical system in terms of Lagrangians and/or Lagrange's equations. Such representations play a role in the methodological formulation for a wide variety of physical problems. We deal with two different approaches to construct Lagrangians for a number of equations. Examples cited cover both point and continuum mechanics. This work will be of special significance to those who would like to study problems of contemporary physics without being directly involved in the rigorous theory of Helmholtz for inverse variational problems. The first procedure chosen by us depends on the method of characteristics as used for solving first order partial differential equations while the second one exploits the symmetries of the Lagrangian and the equation of motion. For simple cases, both approaches are applicable without any modification. However, in more realistic situations the methods need to be supplemented by some ansatz.