有多余坐标的可控完整力学系统的自由运动与初始运动  

FREE MOTION AND INITIAL MOTION OF CONTROLLABLE HOLONOMIC SYSTEM WITH REDUNDANT COORDINATES

作　　者：陈菊[1] 郭永新[2] 梅凤翔[1] Chen Ju;Guo Yongxin;Mei Fengxiang(School of Aerospace,Beijing Institute of Technology,Beijing 100081,China;School of Physics,Liaoning University,Shenyang 110000,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]辽宁大学物理学院,沈阳110000

出　　处：《动力学与控制学报》2019年第5期408-412,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11572145,11572034,11272050)~~

摘　　要：对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统.本文研究有多余坐标的可控力学系统的自由运动与初始运动.首先,需由d′Alembert Lagrange原理并利用Lagrange乘子法建立有多余坐标完整系统的运动微分方程;其次,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件.第三,如果给定运动的初始条件和控制参数,就可以研究系统的初始运动.文末,举例并说明方法和结果的应用.When the parameters of a system are not completely independent,it is called a holonomic system with redundant coordinates.This article explored the free motion and initial motion of a controllable holonomic system with redundant coordinates.Firstly,the differential equations of motion were established according to the d′Alembert Lagrange principle,and the multipliers of constraints were obtained.Secondly,according to the definition of free motion of a constrained system,all the multipliers were set to zero,and the conditions for free motion of the system were obtained.Thirdly,the initial motion of the system was studied,when the initial condi tion of motion and control parameters were given.Finally,an example was given to illustrate the application of this method.

关 键 词：自由运动 初始运动 控制参数 可控系统 

分 类 号：O31[理学—一般力学与力学基础]