Generalized displacements and momenta formulations of an electromechanical plunger

This paper deals with four different derivations of the governing equations of a solenoid plunger with lumped-parameter. Energy-based modeling is employed with extended Hamilton's principle with independent generalized coordinates and generalized momenta in order to be applicable to composite Lagrange's equations. In the electromechanical models, displacements and charges are regarded to be generalized coordinates, mechanical momenta and flux linkages are the generalized momenta. The derived systems of differential equations are solved numerically with the Runge-Kutta method.