引用本文: 姜文安, 刘若冰, 顾叶彤等. 相对运动中一类质点运动方程的同伦摄动解. 力学与实践, 2023, 45(6): 1399-1402.
Jiang Wenan, Liu Ruobing, Gu Yetong, et al. Homotopy perturbation solution of a class of particle motion equations in relative motion. Mechanics in Engineering, 2023, 45(6): 1399-1402.
 Citation: Jiang Wenan, Liu Ruobing, Gu Yetong, et al. Homotopy perturbation solution of a class of particle motion equations in relative motion. Mechanics in Engineering, 2023, 45(6): 1399-1402.

## HOMOTOPY PERTURBATION SOLUTION OF A CLASS OF PARTICLE MOTION EQUATIONS IN RELATIVE MOTION

• 摘要: 相对运动中质点的运动方程大多数是非线性的，其精确显式求解是一个难点。本文基于同伦摄动分析方法，研究了相对运动中一类质点运动非线性微分方程的近似显式解。先构造了系统的同伦方程，再结合Lindstedt–Poincare方法和系统的初始条件，推导了系统自由振动的固有频率，求解了系统的位移近似响应，并通过数值仿真验证了理论分析解的正确性，为相对运动的质点运动方程求解提供了一种新的求解方法。

Abstract: Most of the motion equations of particles in relative motion are nonlinear, and their exact explicit solutions are difficult to obtain. Based on the method of homotopy perturbation analysis, the approximate explicit solutions of a class of nonlinear differential equations of particle motion in relative motion are studied. First, the homotopy equation of the system is constructed, then the natural frequency of the free vibration of the system is derived by combining the Lindstedt–Poincare method and the initial conditions of the system, and the approximate displacement response of the system is solved. The correctness of the analytical solution is verified by numerical simulation, which provides a new solution method for solving the motion equations of relative moving particles.

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