On some applications of Baumgarte's stabilization method

Basically, the behavior of dynamical systems is described with the help of ordinary differential equations. Only for a few systems it is possible to find an analytical solution. Numerical integration methods are used to solve the majority of problems. However, when numerically integrating systems of motion equations with mechanical constraints, the effect of accumulation of rounding errors is possible with implementing a particular finite difference scheme. This can lead to instability of the numerical solution with respect to the constraint equations. To limit the magnitude of such accumulation J. Baumgarte proposed an algorithm to stabilize the constraints during numerical integration. The report is devoted to some applications of this method to modeling, optimization and inverse dynamical problems.