The caotic dynamics of the particle under the influence of independent limiters and vectoral gravitational field

In this thesis, the dynamics of a free oscillator and a point mass moving in the gravitational field are studied. In our model, the oscilating plate motion of the bouncing ball system which is created is simply modelled with a sine function and the transitions of the system from ordinary or regularly defined behavior to chaotic behavior are examined, the results are calculated for the periodic and chaotic behavior of the system at different amplitude values. In cases where the model exhibits chaotic behavior, different parameter values effecting the behavior of the system are examined in detail. In this context, the time series, phase space and Bifurcation diagrams of the system were obtained for cases where the model showed chaotic and regular behavior and the results were interpreted for different parameters. In the results we obtained, it was observed that the system showed periodic behavior when the amplitude 𝐴 < 0,0235 with the same initial conditions, and the system displayed chaotic behavior when 𝐴 > 0,0235. In addition, the effect of the impact parameter on the chaotic behavior formation process for the bouncing ball system under the given conditions is explained and the Bifurcation diagrams for the bouncing ball system under the same conditions are interpreted for the results obtained. All calculations made in this study were obtained by using analytical and numerical methods with programs written by us in Python 3 language.