Second Order Kinematic Constraint Between Two Bodies Rolling, Twisting and Slipping Against Each Other While Maintaining Point Contact

The second order kinematic constraint (acceleration constraint) between two rigid bodies that are rolling, twisting, and slipping against each other while maintaining point contact, is derived by differentiation of the first order constraint and by including the geometry of the surfaces at their contact. This constraint is derived with a view to facilitate the simulation of such motion with general purpose dynamics simulators, and more specifically for the Newton dynamic simulator developed at Cornell University. The constraint is first derived for planar motion and then generalized for motion in three dimensions. Some simple, but representative, examples are presented.