Constrained Based Dynamics Simulation

D’Alembert’s principle, also known as the Lagrange–d’Alembert principle, is a statement of the fundamental classical laws of motion. The principle states that the sum of the differences between the forces acting on a system of mass particles and the time derivatives of the momenta of the system itself projected onto any virtual displacement consistent with the constraints of the system is zero. Thus, in symbols d’Alembert’s principle is written as following,

where

For a system of $n$ links, D’alembert’s equation is