含时变约束的质点系平衡条件讨论  

Analysis on the Balance of Particle Systems with Variable Constraints

作　　者：杨敏[1] 张宇[1,2] 陈占清中国矿业大学深部岩土力学与地下工程国家重点实验室 

机构地区：[1]中国矿业大学理学院,江苏徐州221008 [2]中国矿业大学徐海学院,江苏徐州221008

出　　处：《徐州工程学院学报（自然科学版）》2010年第1期16-20,共5页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(50674087);教育部博士点学科专项基金资助项目(20060290504)

摘　　要：通过运动学分析,并利用隐函数存在定理论证了"欲使含有时变约束的质点系达到平衡状态势必破坏原有的约束";通过一反例说明了含有时变约束的质点系不能达到平衡状态,更不可维持平衡状态.对含有单面约束、非完整约束、参变约束的质点系平衡态的存在性进行了简单分析.对于含有其他复杂约束的质点系,首先应分析质点系是否存在平衡态,如果存在平衡态则可进一步研究平衡的充分条件;如果质点系受到的约束不允许质点系存在平衡态,那么讨论以虚功方程表达的质点系平衡条件的充分性是没有意义的.Through the analysis of kinematics and the exploration of theorem of the existence of implicit function,the conclusion ＂the original constraints will be destroyed if the particle systems with variable constraints reach balance＂ is proved.＂The particle systems with variable constraints can not reach balance,not to mention maintain balance＂ is illustrated by one negative example.The paper briefly discusses the balance of particle systems with unilateral constraints,nonholonomic constraints,and parametric constraints.According to the author,the study of particle systems with other complex constraints should obey the following principle.Whether the balance of the particle systems exists should be analyzed first and foremost,and if it exists,the sufficient condition of balance can be studied further.If under no circumstances will the balance of the particle systems be reached with the certain constrains,the discussion of the sufficient condition of the balance of the particle systems which expressed by the virtual work equation is meaningless.

关 键 词：时变约束 质点系 平衡 虚功方程 

分 类 号：O313[理学—一般力学与力学基础]