Determination of constraint stabilization parameters with multiple roots of characteristic equation

During a numerical integration of motion equations of a constrained mechanical system effect of deviations from initial data can be neglected with the help of Baumgarte stabilization method. According to this method first time derivatives of constraint equations are not considered as first integrals and are equated to an arbitrarily linear form of constraints themselves. The coefficients of these forms are called perturbation parameters. So, the problem of constraint stabilization is reduced to a problem of finding an appropriate range of perturbation parameters' values. This problem can be solved by obtaining these values with the help of stability conditions. The procedure of evaluation is getting even more easier if the perturbation coefficients correspond to the multiple root case of its characteristic equation. © 2019 IOP Publishing Ltd. All rights reserved.