Study On Symmetry Theories Of Electromechanical Devices

Analysis mechanics research mechanics related problems,using generalized coordinates to describe variables of the particle system.The principle of virtual displacement is the basis of the analysis of statics and the principle d'Alember-Lagrange is the basis of analytical dynamics.Symmetry theories are to study the invariance of system under certain motion and transformation.Symmetry is common in nature and daily life,and it reflects some hidden physical laws of system.Symmetry theories have been widely used in mathematics,mechanics,physics,mechanics and mechanics.There is a close relationship between symmetries of system and the conserved quantities,and to study the symmetries of system and the conserved quantities can be used to solve motion differential equation of system.In this paper,circuits and electromechanical systems are studied,and the Nielsen's equations of electromechanical system are given.At the same time,applying the Nielsen's equations of electromechanical system to establish the differential equation of automobile electromagnetic suspension system,the symmetries and conserved quantities of the system are studied,and the dynamic response of the system is solved by using the conserved quantities.Firstly,the Nielsen's equations of the circuit are given by the Kirchhoff principle of the circuit and the similarity between the circuit system and the mechanical system.Using the Nielsen's equations of the circuit and the Nielsen's equations of the mechanical system,the mechanical part and the circuit part of the electromechanical system are studied,and the Nielsen's equations are given.Secondly,the electromagnetic suspension system of vehicle is divided into two types according to the vehicle motion,and the motion differential equations are established by using the Nielsen's equations of the electromechanical system in the form of two kinds of vibration.Thirdly,the Noether symmetry and the conserved quantities of automotive electromagnetic suspension system are studied.By introducing the infinitesimal transformations and infinitesimal generators,the Hamilton auto quantitative electromagnetic suspension system of is divided,and the system criterion,Noether equation,Killing equations and the Noether theorem are given in Noether generalized quasi symmetric of the system.By solving the Killing equations and the Noether identity of the system,the generator and the corresponding norm function of the system are obtained,and then the conserved quantity of the system is obtained.Then,the Lie symmetries and conserved quantities of two kinds of vehicle electromagnetic suspension systems are studied.Under the condition of nonsingular the differential equations,introducing the infinitesimal transformation and an infinitesimal generator,study on invariance of differential equation of vehicle electromagnetic suspension system.The Lie symmetry criterion,Lie symmetry determination equation and Lie theorem are given,and then the Lie symmetry conservation quantity is given.At last,to solve symmetric solutions of differential equations by using conserved quantities of the system.The input signal is given and the displacement response and velocity response of the system are given by the symmetric solution of the system.The vibration modes of the system under different feedback input signals are studied.