Minimum-time control problem for elastic and visco-elastic interaction between body and surface

Two minimum-time control problems are considered for the mechanical system consisting of material point and obstacle surface which interact with each other by the means of the elastic or visco-elastic spring. Interaction time interval is determined by physical conditions of contact. The dependences are studied of full interaction time and restitution coefficient on visco-elastic spring properties. The Python program is developed and the “material point–obstacle surface” system behavior modelling is conducted.