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有多余坐标的完整系统形式不变性导致的新守恒量
引用本文:许学军,梅凤翔,秦茂昌.有多余坐标的完整系统形式不变性导致的新守恒量[J].上海力学,2004,25(2):286-290.
作者姓名:许学军  梅凤翔  秦茂昌
作者单位:北京理工大学力学系,北京理工大学力学系,北京理工大学力学系 北京 100081 浙江师范大学物理系,浙江 金华 321004,北京 100081,北京 100081
基金项目:国家自然科学基金资助项目(10272021)
摘    要:研究有多余坐标的完整力学系统由形式不变性直接导出的新型守恒量。用有多余坐标的双面理想完整约束力学系统的运动微分方程和约束方程在无限小变换下的形式不变性,给出系统形式不变性的定义和判据。得到形式不变性导致守恒量的条件以及守恒量的形式,并给出三种特殊情形下的推论。举例说明结果的应用。

关 键 词:多余坐标  完整系统  形式不变性  守恒量
文章编号:0254-0053(2004)02-286-5
修稿时间:2003年11月13

A New Conserved Quantity Constructed by Form Invariance for Holonomic Systems with Redundant Coordinates
XU Xue-jun,MEI Feng-xiang,QIN Mao-chang.A New Conserved Quantity Constructed by Form Invariance for Holonomic Systems with Redundant Coordinates[J].Chinese Quarterly Mechanics,2004,25(2):286-290.
Authors:XU Xue-jun  MEI Feng-xiang  QIN Mao-chang
Abstract:A new conserved quantity constructed directly by using the form invariance for a holonomic system with redundant coordinates was presented. The definition and the criterion of the form invariance of the system were obtained by relying on the fact that the differential equations of motion and the constrained equations of the bilateral ideal holonomic mechanical system with redundant coordinates preserve an invariance under the infinitesimal transformations. The condition under which the form invariance can lead to a conserved quantity and the form of the conserved quantity were deduced, and three corollaries in special cases were given. Two examples are finally given to illustrate the application of the results.
Keywords:redundant coordinates  holonomic system  form invariance  conserved quantity  
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