Bifurcation And Chaos Of The Pole And Plate In The Electromagic Field

Bifurcation and Chaos is the most important and most basic features in nonlinear systems,almost all involved in the field of nonlinear science, there is a bifurcation phenomena and chaotic motion. Based on the analysis and summary of nonlinear differential bifurcation and chaotic dynamical systems on the basis of the status quo in the electromagnetic conductivity slender bar and beam-plate nonlinear behavior were studied. This paper mainly on the following aspects of content.Firstly, summed up the current domestic and foreign scholars on the bifurcation phenomenon of chaotic motion and the issue of the status quo, have fork bifurcation expounded, Hopf bifurcation and saddle-node bifurcation balance bifurcation and three closed orbit bifurcation, homoclinic orbit (heteroclinic track) bifurcation conditions. Hamilton systems and gives the homoclinic tracks and the heteroclinic orbit calculation. Melnikov function briefly introduced the solution.Secondly, the electromagnetic field in a slender bar Analysis, have been under slender bar electromagnetic field equations of motion and against static mechanics, linear dynamics and nonlinear dynamics three models, a study of bifurcation.Finally, Melnikov method used in the horizontal magnetic field and mechanical loads under common beam-plate nonlinear behavior, first of all, on non-disturbance system were analyzed by the system is unperturbed Hamiltonian system, in accordance with its energy function Hamilton obtained its close orbital parameters equation, and gives the amplitude and its system the relationship between volume and further disturbances system in the calculation of the bifurcation of the market Melnikov function, the simple existence of Melnikov function of the system that existed Smale horseshoe transform the sense of chaos, and further chaos when transverse magnetic field presence with the outside world mechanical strength of the relationship between the rate.