The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field

In this paper, a constant of motion of charged particle motion inhomogeneous electromagnetic field is derived from Newton's equations and thecharacteristics of partial differential equation, the relatedLagrangian is also given by means of the obtained constant of motion. Bydiscussing the Lie symmetry for this classical system, this paperobtains the generalexpression of the conserved quantity. It is shown that the conservedquantity is the same as the constant of motion in essence.