首页|THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS
THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS
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This paper deals with the problem of limit cycles for the whirling pendulum equation(x)=y,(y)=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.
whirling pendulumlimit cycleMelnikov functionPicard-Fuchs equationChebyshev system
杨纪华
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School of Mathematics and Computer Science,Ningxia Normal University,Guyuan 756000,China
Ningxia Basic Science Research Center of Mathematics,Yinchuan 750000,China
Natural Science Foundation of NingxiaNational Natural Science Foundation of China
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