Generalized Forces - D'Alembert's Principle

D'Alembert's Principle

D'Alembert formulated the dynamics of a particle as the equilibrium of the applied forces with an inertia force (apparent force), called D'Alembert's principle. The inertia force of a particle, P_i, of mass m_i is

where A_i is the acceleration of the particle.

If the configuration of the particle system depends on the generalized coordinates q_j, j=1,...,m, then the generalized inertia force is given by

D'Alembert's form of the principle of virtual work yields