UNEVEN ROTATION OVER A PLANE CIRCULAR ORBIT AROUND THE VERTICAL AXIS OF A CHARGED METAL BALL WITH ACCOUNT FOR DISSIPATIVE FORCES

Abstract

Purpose. The nonlinear dynamics of a charged metal ball rotating over the horizontal plane is described and the solution of the nonlinear differential equation is analyzed, which takes into account both bremsstrahlung electromagnetic radiation and traditional resistance forces resulting from the viscosity of the continuum (viscous friction) and dry friction in the hinge joint. Methodology and Approach. The research method is based on the compilation of a motion equation using the principle of preserving the hollow power of the system under study. Results. A dynamic motion equation is obtained and its analytical solution is found in a parametric form. Theoretical and Practical implications. The mathematical description of the dynamics of the movement of a charged metal ball over a circular orbit is proposed and a solution to the resulting equation/analysis can be practically used in the study of the motion of the planets of the Solar System.

Keywords

• uneven motion
• centrifugal force
• bremsstrahlung radiation