Nonconservative Lagrangian and Hamiltonian mechanics

Abstract

Traditional Lagrangian and Hamiltonian mechanics cannot be used with nonconservative forces such as friction. A method is proposed that uses a Lagrangian containing derivatives of fractional order. A direct calculation gives an Euler-Lagrange equation of motion for nonconservative forces. Conjugate momenta are defined and Hamilton's equations are derived using generalized classical mechanics with fractional and higher-order derivatives. The method is applied to the case of a classical frictional force proportional to velocity. \textcopyright{} 1996 The American Physical Society.