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.
Science Fair Project done By Konstantin Y. Batygin