Lie symmetries and conserved quantities of the singular mechanico-electrical coupling systems

Abstract

In this paper, the Lie symmetry theory of singular mechanico-electrical coupling systems is studied in phase space. Firstly, the Hamilton canonical equation of singular mechanico-electrical coupling systems is established through energy; Secondly, considering the inherent constraints brought by singularity, the determining equations, definitions, structural equations and conserved quantities of Lie symmetry are all given; Finally, an application example is given. It is shown that if the structural equation of Lie symmetry is just right the criterion equation for Noether symmetry, then the Lie symmetry can lead to the conserved quantity of Noether type; if the structural equation of Lie symmetry does not involve the Hamiltonian function, the conserved quantity of non-Noether type can be obtained only through finding the invariant of symmetric group.

Keywords

Singular mechanico-electrical coupling systems Lie symmetries structural equations conserved quantities

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