THE CONDITIONS OF TRANSITION BETWEEN REGULAR AND CHAOTIC MOTION OF A CHARGED DOUBLE PENDULUM IN A UNIFORM ELECTROSTATIC FIELD

We study the dynamics of the planar double pendulum with electric charges attached to its point masses. These charges interact with a uniform external electrostatic field. We derive the Hamilton equations of motion of the system. Using numerical integration of these equations, we derive two- and three-dimensional Poincaré sections of the phase space and examine scenarios when the pendulum switches between regular and chaotic motion. It is shown in this paper that such a transition depends both on the interaction strength in the system and on the relative sign of the two charges attached to the pendulum. We find out that the pendulum motion is nearly regular both in the weakand strong-field scenarios, while chaotic behaviour is present at intermediate coupling strengths. These results are consistent with those known for the gravitationally driven double pendulum. When the charges have like signs, the invariant tori are largely restored as the field grows stronger; when the charges have opposite signs, however, chaotic mixing of trajectories persists even at high values of the electrostatic coupling. We propose the hypothesis that the measure of the surviving invariant tori decreases faster as a function of the interaction strength for oppositesigned charges than for like-signed charges.