Dynamic Analysis of Vertical Excited Pendulum in Magnetic Field
Based on the practical application of energy harvesting,a mathematical pendulum model in a magnetic field is constructed,and its dynamic behavior is analyzed in depth.The purpose of this study is to provide theoretical sup-port for the optimal selection of working performance parameters of engineering pendulum equipment.Firstly,the potential well curve is derived from the potential energy function,and the influence of the potential well and barrier on the dynamic characteristics of the system is discussed.Then,using the Melnikov function method,this study not only solves the homoclinic trajectory of the system and the critical conditions for the generation of chaos in the Smale sense,but also reveals the relationship between the amplitude and the frequency of the simple pendulum system,and proposes a numerical method to calculate the homoclinic bifurcation curve,and successfully draw the bifurcation curve.Finally,by using the analytical tools such as single-parameter bifurcation,Lyapunov exponent,phase trajectory diagram,Poincare cross section diagram and bifurcation diagram in the two-parameter plane,two paths of the evolu-tion of the oscillating system to chaos are shown:period-doubling bifurcation and saddle-junction bifurcation.In addi-tion,the global motion laws of this kind of simple pendulum system,such as period doubling bifurcation,attractor doubling,saddle junction bifurcation,etc.,are also revealed,and the influence of related parameters on the working performance of the engineering system and the action mechanism are further clarified.
magnetic pendulumbifurcationchaostwo-dimensional parameter plane
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