Dynamics of a Double Mathematical Pendulum with Variable Mass in Dimensionless Coordinates

The article presents an analysis of the dynamics of a double mathematical pendulum with variable mass. In the analyzed system, with time, under the influence of gravity, the mass of the upper member of pendulum decreases and the mass of the lower member of pendulum increases. The total mass of the system doesn't change. For the analysis introduced dimensionless time and dimensionless parameters, which allows the presentation of the equations of motion in dimensionless form. It has been shown that the change of mass in the system has a significant impact on the dynamics. The increase in mass of the lower member reduces the amplitude of vibration of the pendulum. The numerical calculations were performer in Mathematica package.