THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS  

作　　者：杨纪华 Jihua YANG(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan,756000,China;Ningxia Basic Science Research Center of Mathematics,Yinchuan,750000,China)

机构地区：[1]School of Mathematics and Computer Science,Ningxia Normal University,Guyuan,756000,China [2]Ningxia Basic Science Research Center of Mathematics,Yinchuan,750000,China

出　　处：《Acta Mathematica Scientia》2024年第3期1115-1144,共30页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of Ningxia(2022AAC05044);the National Natural Science Foundation of China(12161069)。

摘　　要：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.

关 键 词：whirling pendulum limit cycle Melnikov function Picard-Fuchs equation Chebyshev system 

分 类 号：O153.3[理学—数学]