Mechanical memory elements: Modeling of systems with position-dependent mass revisited

The purpose of this paper is two-fold. First, it is shown that systems in which mass is changing with position belong to the family of memory elements. Memory elements have originally been introduced in the electrical domain to provide a logical extension of the resistor, inductor, and capacitor. Secondly, it is shown that straightforward application of the classical Lagrangian and Hamiltonian frameworks to describe these type of elements generally leads to erroneous results. To overcome these problems, a port-Hamiltonian formulation is proposed. The developments are illustrated and motivated using the elementary cable-reel system.