Symmetry And Conserved Quantities Of Controllable Nonholonomic System And Electrical Power Systems

The main purpose of this dissertation is to study the problems of symmetries and conserved quantities of controllable nonholonomic systems and mechanico-electrical dynamical systems, based on the invariance of the Hamilton action under the infinitesimal Lie group transformation. It includes the theories of Noether symmetries and Lie symmetries of the systems, and the geometric theory of Noether symmetry of mechanico-electrical dynamical system. This dissertation contains three chapters.In chapter one, the symmetries and conserved quantities of controllable nonholonomic systems are analyzed. Introducing the Lie group analytic method into controllable nonholonomic system, we present the variation principle of the system, the Noether symmetry, the generalized Noether symmetry, the inverse problem of Noether symmetry;Lie symmetry and the inverse problem of Lie symmetry.In chapter two, the symmetries and conserved quantities of mechanico-electrical dynamical systems are studied. We present the fundamental theories of Noether symmetries and conserved quantities of mechanco-electrical dynamical systems, including variation principle of the system, Noether symmetry transformation, Noether quasi-symmetry transformation, generalized Noether quasi-symmetry transformation, Killing equations, Noether theorem, the form of conserved quantity. And then the basic theory of Lie symmetry is advanced, including the determining equation, structure equation and the form of conserved quantity.In chapter three, the geometric theory of Noether symmetry of mechanico-electrical dynamical system is investigated. Introducing the fundamental knowledge of modern differential geometry, we present the geometric descriptions of Lie symmetry of the system.