Certain cases of the classical collision theory

The paper analyzes the elastic-plastic collision of a complex system of two rigid beams with a rigid disk between them. A rigid beam strikes this system horizontally. In the problem, immediately after the impact, we deal with seven unknown velocities and force impulses. The unknowns were determined by setting up a system of seven equations and solving it computationally using the Mathematica package.
Special cases of this solution were analyzed. In the second part of the report, the case where the lower beam of the system is loaded with a given force impulse was solved. A rich bibliography of the subject is also provided. In the paper, we analyze a rigid material system consisting of two horizontal beams and a disk between them. The beams are located in perfectly smooth horizontal guides.
Additionally, we assume no slip between the beams and the disk after the lower beam of the system is struck by a horizontal rigid beam. The collision is elastic-plastic and the coefficient of restitution is given. There are seven unknown velocities and force impulses in the problem.
To determine them, seven equations of collision theory were formulated and solved using the Mathematica package. Special cases of plastic and perfectly elastic collisions were analyzed. Kinetic energy losses were determined, and in the case of an elastic collision, the correctness of the solution was verified. (…)

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