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Nonlinear oscillations of a pendulum wrapped around a cylinder

The large oscillations of a pendulum are studied. The pendulum is a material point that is suspended on an elastic cord with nonlinear characteristics. The mass of the cord is accepted. It is wrapped around a perfectly rigid and fixed cylinder. The system has two degrees of freedom. Nonlinearity is due to a geometric and physical nature. A system of two differential nonlinear equations is derived. A numerical solution was performed with the mathematical package MATLAB. The laws of motion, the generalized velocities and accelerations and the phase trajectories are obtained. In order to continue the task by preparing an actual model and conducting experimental research, the projections of the velocity and acceleration of the material point along the horizontal and vertical axes, as well as their magnitudes, are determined. The obtained results are presented graphically and analysed in detail.