Contact dynamics modeling remains an intensive area of research with new applications emerging in robotics, biomechanics and multibody dynamics areas. Many formulations for contact dynamics problem have been proposed. The two most prominent categories include the discrete approach, which employs the impulse-momentum relations, and the continuous approach, which requires integration of dynamics equations through the contact phase. A number of methods in the latter category are based on an explicit compliant model for the contact force. One such model was developed by Hunt and Crossley three decades ago who introduced a nonlinear damping term of the form λxn into the contact force model. In addition to proposing the general form of this damping component of the contact force, Hunt and Crossley derived a simple expression for relating the damping coefficient λ to the coefficient of restitution e. This model gained considerable popularity due to its simplicity and realistic physics. It also spurred new research in the area, specifically on how to evaluate the damping coefficient λ. Subsequently, several authors put forward different approximations for λ, however, without clearly revealing the range of validity of their simplifying assumptions or the accuracy limitations of the resulting contact force models. The authors of this paper analyze the various approaches employed to derive the damping coefficient. We also evaluate and compare performance of the corresponding models by using a meaningful measure for their accuracy. A new derivation is proposed to calculate more precisely the damping coefficient for the nonlinear complaint contact model. Numerical results comparing all models are presented for a sphere dropping on a stationary surface.

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