The objective: The subject of the study was a chaotic particle motion initiated by a nonlinear periodic force in a mechanical system. The appearance of chaotic dynamics in simple mechanical systems, is a fundamental classical phenomena.

Non-linear oscillations were simulated through computer modeling. The computer model was realized as a sequence of matrix multiplication. Each matrix describes linear and non-linear oscillations of a mechanical body under external forces

The result of the matrix multiplication was a chaotic motion performed by a particle in the presence of linear and non-linear forces.

This type of particle action is called the "beam-beam effect." It is one of the main reasons that limits the intensity of a particle collider.

The project is the study of particle motion inside a collider under external linear and nonlinear forces.

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