Damping Potential, Generalized Potential, and D’Alembert’s Principle

An alternative form of Lagrange’s equations is used to introduce a new equation for deriving a monogenic force from a velocity-dependent potential. Based on this and corresponding to a linear damping force, a bilinear potential function is introduced, which obviates the need for a dissipation function to represent a damping force. This idea is then generalized by introducing a generalized potential function which allows D’Alembert’s principle, Lagrange’s equations, and Hamilton’s principle to be represented solely in terms of potential functions. The introduced potential functions and equations are used to derive motion equations of a floating body.