Solving procedure for the dynamics of charged particle in variable (time-dependent) electromagnetic field

Abstract

In this challenging analytic survey, we present a new approach for solving equations of the dynamics of a charged particle (describing its motion in variable, time-dependent electromagnetic field) which has been applied earlier in various fields of mechanics for solving equations of hydrodynamics, Euler–Poisson equations of rigid body rotation and even in celestial mechanics (solution of equations of small body’s motion in the CR3BP problem near librations points): a new type of the solving procedure is implemented in all of these equations as well as in case of solving momentum equation for the aforementioned dynamics of a charged particle, determined by Lorentz force in non-relativistic case. Meanwhile, in each case the system of momentum equations has been successfully solved analytically. The main result of the current research should be formulated as follows: the analytic algorithm is pointed out for solving momentum equation, which has been reduced to the analytical solution of three nonlinear ODEs with respect to the components of velocity of the particle. Moreover, absolutely new partial analytical solutions have been obtained for the special cases of magnetic field (with zero electric field’s components). In addition to this, we conclude that system of Lorentz momentum equations for dynamics of a charged particle has not the analytical presentation of solution in case of nonzero, time-dependent electric field.