Research On The Application Of Discrete Variation Principle In Electro-Mechanical Coupling Systems

The variation method is both ancient and modern science tools, but plays a keyrole, and the discrete variation principle and Euler-Lagrange equation are derived byintroducing discrete action of the system. In1983, famous physicist T.D.Lee putforward a new thought of the discrete mechanics variation, Lee first studied theversion of regarding the time as a discrete dynamical variable. The modern discretevariation principle is gradually to close the structure preserving, and then foreignscholars put forward the variation integrators method, and gradually become theresearch focus in the field of discrete mechanics.With the development of modern science and technology, mechanical systemand the electromagnetic system are more and more closely linked, electro-mechanicalcoupling systems meet the eyes everywhere in our daily life, such as: generators,motors, maglev train and electrical experiment measuring instrument and so on. Thebasic characteristics of the electro-mechanical coupling systems is the conversionbetween mechanical energy and electromagnetic energy, and involved the content isvery wide, not only covers the mechanical system and the electromagnetic system,but also includes a variety of structures interconnected instrumentation systems. Theelectro-mechanical coupling systems play an important role in sensor, speaker,remote control device, automatic control system and a large number of automationsystems and so on.This paper mainly uses the discrete variation method, and discusses the theapplication of discrete variation principle in electro-mechanical coupling systems,establish the discrete Lagrange-Maxwell equations. Chapter two briefly introducesthe discrete variation method and implementation of variation integrators, mainlycontain the midpoint rule, Verlet method,explicit symplectic partitioned Runge-Kuttamethod and so on, and then calculate the pendulum example, verify the application ofdiscrete variation method in the dynamical system is feasibility and rationality.Chapter three uses the electro-mechanical analysis dynamics method for the electro-mechanical coupling system’s physical modeling and theoretical analysis, andthen describe the dynamics equation of the electro-mechanical coupling systems;Through the mechanical system and the electromagnetic system to establish auniform relationship model to simulate the two systems. Chapter four uses thediscrete variation method establish the describe Lagrange-Maxwell equation, andwith RLC spring coupling system through numerical calculation, the main method ofdiscrete processing for electro-mechanical coupling systems is Verlet method, thengive the variation integrators, set the middle variable, put these into the discreteEuler-Lagrange equation of the electro-mechanical coupling systems, the calculationresults accord with characteristics of motion of the system, we have explain therationality on application of discrete variation method in the numerically research ofthe electro-mechanical coupling systems. Chapter five shows the numericalcalculation of the electro-mechanical coupling systems by using the symplecticRunge-Kutta methods, and numerically studies the movement of the plate in the RLCcircuit spring coupled system and the current changes, and on this basis, the forminvariance of Noether sense is studied by using the symplectic Runge-Kutta. Its resultis consistent with the discrete variation method. Through the comparison wedemonstrates the discrete variation method is reasonable and effective in studying themechanical-electrical coupled systems. Chapter six summarized the main results ofthis paper, and prospects for future study.