A New Lagrangian and a New Lagrange Equation of Motion for Fractionally Damped Systems

Abstract

All dynamic systems exhibit some degree of internal damping. Recent investigations have shown that a fractional derivative model provides a better representation of the internal damping of a material than an ordinary derivative model does. For a survey of fractional damping models and their applications to engineering systems, the readers are referred to Rossikhin and Shitikova 1 and the references therein. Traditionally, the Newton’s law is used to model such nonconservative systems, and when a Lagrangian, Hamiltonian, variational, or other energy-based approach is used, it is modified so that the resulting equations match those obtained using the Newtonian’s approach.