State space representation of holonomic and nonholonomic constraints resulting from rolling contacts

The control of mechanical systems subjected to rolling contacts is studied. Rolling contacts result in both holonomic and nonholonomic constraints. The focus of this paper is on formulating the differential motion equations and algebraic constraint equations into the standard state space representation of dynamic control systems. The position-level holonomic constraints are approximated by a set of velocity-level constraint equations that asymptotically converge to the original holonomic constraints. The approximation removes the numerical instability and ensures the satisfaction of holonomic constraints, particularly in computer simulations. Further, the approximation eliminates the need to solve holonomic constraints either analytically or numerically. The resulting approach makes it possible to treat systems with holonomic constraints, systems with nonholonomic constraints, and systems with both holonomic and nonholonomic constraints in a unified framework. The approach facilitates the computer simulation of mechanical systems with rolling constraints.