An Improved 'Heuristic' Approximation for the Period of a Nonlinear Pendulum: Linear Analysis of a Classical Nonlinear Problem

A. Belendez; A. Hernandez; T. Belendez; A. Marquez; C. Neipp

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An Improved 'Heuristic' Approximation for the Period of a Nonlinear Pendulum: Linear Analysis of a Classical Nonlinear Problem

机译：非线性摆周期的改进的“启发式”逼近：经典非线性问题的线性分析

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摘要

A new analytical approximate expression for the period of the simple pendulum is obtained by using a heuristic but pedagogical derivation. This formula depends on two parameters obtained by comparing term-by-term the power-series expansions of the approximate and exact expressions for the period. This formula is compared with others in the literature and the numerical results obtained show that the published approximations are not nearly as good as the new expression proposed in this paper.

机译：通过使用试探法和教学法推导，获得了简单摆周期的新解析近似表达式。该公式取决于两个参数，该参数通过逐周期比较该期间的近似表达式和精确表达式的幂级数展开而获得。将该公式与文献中的其他公式进行比较，获得的数值结果表明，所发表的近似值不如本文中提出的新表达式好。

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《International journal of nonlinear sciences and numerical simulation》 |2007年第3期|共6页
作者
A. Belendez; A. Hernandez; T. Belendez; A. Marquez; C. Neipp;
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正文语种 eng
中图分类数值分析;
关键词
Nonlinear oscillator; Simple pendulum; Large-angle period; Approximate solutions;

机译：非线性振荡器;简单摆;大角度周期;近似解;

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7. An improved 'heuristic' approximation for the period of a nonlinear pendulum: linear analysis of a classical nonlinear problem [O] . Beléndez Vázquez, Augusto, Hernández Prados, Antonio, Beléndez Vázquez, Tarsicio, 2007

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An Improved 'Heuristic' Approximation for the Period of a Nonlinear Pendulum: Linear Analysis of a Classical Nonlinear Problem

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