光滑水平面内弹簧振子运动的周期性问题  

The periodicity of motion of spring vibrator confined to horizontal frictionless plain

作　　者：陈丽娟[1] 鲁世平[1] CHEN Li-juan;LU Shi-ping(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《高校应用数学学报（A辑）》2022年第4期448-454,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11271197)。

摘　　要：弹簧振子在水平面上的运动是工程学中一种非常重要的非线性运动,其动力学模型是理论力学中不可积系统的典型模型.由于振子的运动微分方程具有非线性性和强奇性,难以求解,文中利用重合度理论对弹簧振子运动的数学模型的周期性进行了研究,得到了该模型在一定条件下存在周期正解的结论,验证了所给条件的可行性和所得结果的准确性.The motion of spring vibrator in the horizontal plane is a very important nonlinear motion in engineering.Its dynamic model is a typical model of non integrable system in theoretical mechanics.Due to the nonlinearity and strong singularity of the differential equation of motion of the oscillator,it is difficult to find the solution.In this paper,the periodicity of the model for motion of spring vibrator is discussed.A result on the existence of periodic solution to the model is obtained,and the feasibility of the initial condition and result given in the paper is verified.

关 键 词：弹簧振子 奇性 周期正解 重合度理论 

分 类 号：O193[理学—数学]