Nonstandard Lagrangians and branching: The case of some nonlinear Liénard systems

Abstract

We propose a new form of Lagrangian that shows branching for the associated Hamiltonian and has relevance to the quadratic type and mixed linear-quadratic Liénard-type nonlinear dynamical equations on adjusting the underlying parameters. Non-uniqueness of the Lagrangian is pointed out and a particular one when Fourier transform is demonstrated to depict a momentum-dependent quantum-like mass system when expanded binomially.