Generalized Lagrange--d'Alembert principle (Q2853205)

A variant of the Lagrange--D'Alembert principle for mechanical systems with holonomic constraints is formulated by introducing generalized coordinates in the normal direction to the tangent space of the configuration manifold. The sum of the virtual works of the active forces, inertial forces and reaction forces is equal to zero, where a virtual displacement is taken to be the sum of the classical virtual displacement and a virtual displacement in the normal direction. In such a way, the constrained forces are calculated from the equations of dynamical equilibrium.