An implicit multistage integration method including projection for the numerical simulation of constrained multibody systems (Q1271108)

The authors consider the equations of motion of a constrained holonomic multibody system, and investigate direct integration schemes for the generalized velocities and coordinates. They discuss the stability of a number of methods of numerical solution and obtain third-order accuracy with a two-stage Runge-Kutta method, giving conditions for its stability. It is pointed out that it is necessary to use constraint equations, otherwise the discretisation results in physically meaningless solutions, and a discussion is given of possible types of constraints.