Nonlinear viscoelastic model of the collinear collision

Nonlinear viscoelastic model of a body collinear collision with a fixed obstacle is investigated. The first integral of the motion equation is obtained. The coefficient of restitution and kinetic energy loss dependences from the impact velocity are analytically constructed. The solution of body motion equation during collision is obtained as the quadrature formula with respect the special Lambert W function. The mathematical simulation results are presented.