Wandering symmetries of the Lagrange's equations

Abstract

The dynamic process can be in equal degree adequately prototyped by a family of Lagrange's systems. Symmetry group wanders on this family: systems are transformed from one into another. In this work we show that under determined condition the first integral can be obtained by a simple calculations on some of such groups. The main purpose of the work is to show usefulness of wandering symmetry concept. The considered example: flat motion of a charged particle in magnetic field in presence of viscous friction. With the help of three wandering symmetry first integral is calculated.

Keywords

• the Lagrange's equations
• variational symmetries
• divergental symmetries
• conformal symmetries
• wandering symmetries
• the first integrals