分析力学中的高阶Nielsen算子和高阶Euler算子

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Nielsen’s and Euler’s Operators of Higher Order in Analytical Mechanics

摘要: 本文提出与研究完整约束系统和高阶非完整约束系统相关的高阶Nielsen算子和高阶Euler算子的定义,建立表示两类算子之间关系的若干定理,应用这些定理得到高阶约束系统的若干新型运动微分方程,最后举例说明新方程的应用。

Abstract: In this paper, the definitions of Nielsen's and Euler's operators of higher order are presented. These operators are concerned in analysis for systems with holonomic constraints and non-holonomic constraints of higher order. Some theorems that indicating relation between the two operators are established. Moreover, using the theorems, the new equations of mechanical systems with constraints of higher order are derived. Finally, an example is given.

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