Dynamics modeling of nonholonomic mechanical systems: Theory and applications

The paper presents a dynamics modeling method that enables generation of motion equations for mechanical systems subjected to nonholonomic constraints of arbitrary order. The method referred to as generalized program motion equations (GPME) method includes, as special cases, modeling methods based on Lagrange's equations with multipliers, Appell's, Maggi's, or Nielsen's equations. The theoretical framework we present is illustrated with an example from a control field. We selected the control application, since the dynamic models are directly applicable in control algorithm designs.