Abstract

Periodic solutions of pendulum-type ODE systems are considered. Finding such solutions is a classical problem in mechanics. Numerous methods are available for computing periodic solutions, and these methods have existed as long as the problems themselves. However, they were designed for manual calculation, and attempts to program them in computer algebra systems (CAS) are sometimes ineffective. For computing such solutions, we propose a method intended for CAS. The method is based on the use of high-order variational equations and symbolic differentiation. It is shown on a number of examples that all computations are reduced to operations with polynomials.

中文翻译：

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小参数摆型系统周期解的计算

摘要

考虑了摆型ODE系统的周期解。寻找这样的解决方案是力学中的经典问题。有许多方法可用于计算周期解，只要问题本身存在，这些方法就已经存在。但是，它们是为手动计算而设计的，尝试在计算机代数系统（CAS）中进行编程有时会无效。为了计算此类解决方案，我们提出了一种针对CAS的方法。该方法基于使用高阶变分方程和符号微分。在许多示例上显示，所有计算都简化为多项式运算。