Velocity-surface stability of a moving charged particle in a controlled electromagnetic field

Abstract

Given the equation motion of a moving charged particle in a controlled electromagnetic field, this paper proves that its velocity-trajectory motion converges to an specified velocity-surface in the 3-D Euclidean dimensional space. This is basically realized by just manipulating the electric field of an electromagnetic field. Lyapunov theory is invoked to test our statement; besides, a numerical example is provided to support our theoretical contribution. Finally, we consider that the exposition of this paper could be of interest to undergraduate students.