New methods in collision of bodies analysis

The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately, but much better than the penalty method. Namely the energy method exactly satisfies the conservation of energy law, whereas the kinematic method exactly satisfies the condition of impenetrability of bodies. Both these methods are superior in comparison with the penalty method, which is demonstrated by the results of several numerical examples.