Second-order contact kinematics for regular contacts

Second-order contact kinematics for regular contacts, such as surface-surface, curve-curve, curve-surface, and vertex-surface, are formulated in a unified framework, extending Montana´s (1988) first-order contact kinematics for surface-surface contact only. Given two rigid bodies in contact with each other, the contact kinematics is the mathematical expression of the relative motion between them and the five dimensional contact coordinate vector. Second-order contact kinematics describes the second-order derivative of the contact coordinate vector in terms of the derivative of the relative twist. The result can be directly applied to geometric integration of contact dynamics.