时间尺度上非迁移完整力学系统的Lagrange方程与Nielsen方程

Lagrange equations and Nielsen equation of non-shifted holonomic mechanical systems on time scales

研究时间尺度上非迁移完整力学系统的Lagrange方程与Nielsen方程。首先,建立时间尺度上非迁移Hamilton原理;其次,基于非迁移Hamilton原理,导出时间尺度上非迁移一般完整力学系统的Lagrange方程;再次,由非迁移Lagrange方程导出时间尺度上单自由度非迁移完整力学系统的Nielsen方程;最后,给出了两个算例以说明结果的应用及其有效性。

This paper investigates Lagrange equations and Nielsen equations of non-shifted holonomic mechanical systems on time scales.Firstly,the non-shifted Hamilton principle on time scales was established.Secondly,based on the non-shifted Hamilton principle,the Lagrange equations of general non-shifted holonomic mechanical systems on time scales were derived.Thirdly,the Nielsen equations of one-degree-of-freedom non-shifted holonomic mechanical systems on time scales were derived from the non-shifted Lagrange equations.Finally,two examples were given to illustrate the application and validity of the results.