Mobility of bodies in contact - II: How forces are generated by curvature effects?

We investigate the contact forces generated by 2nd order effects for a body B, in frictionless contact with finger bodies A_1,..., A_k. A simple paradox shows that rigid body models are inadequate to explain how contact forces are generated by 2nd order effects. A class of configuration-space based elastic deformation models are introduced, and are shown to explain the restraining forces produced by surface curvature. Using these elastic deformation models, we prove that any object which is kinematically immobilized to 1st or 2nd order is also dynamically locally asymptotically stable with respect to perturbations.