全国纪念非完整力学诞生100周年学术会议简况

中国力学学会一般力学专业委员会、中国兵工学会应用力学专业委员会、湖南省力学学会、全国高校理科理论力学研究会、全国高校数学物理方法研究会、全国师专理论力学研究会联合发起主办的“全国纪念非完整力学诞生100周年学术会议”于1994年10月4日至8日在开封市河南大学召开。陈滨教授、梅凤翔教授任会议主席,中国科学院院士、中国力学学会理事长王仁教授任会议名誉主席;王仁院士和会议副主席牛青萍教授分别发来了贺信、贺电,祝本次会议圆满成功、各位代表身体健康。     

Lagrange系统一类新型的非Noether绝热不变量——Lutzky型绝热不变量

研究了Lagrange系统的Lie对称性摄动与新型的非Noether绝热不变量. 列出了未受扰Lagrange系统的Lie对称性导致的Lutzky型精确不变量；基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Lagrange系统Lie对称性的摄动，得到了系统的一类Lutzky形式的绝热不变量.举例说明方法和结果的应用.     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.     

Chetaev型约束力学系统Appell方程的Lie对称性与守恒量

研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用. 关键词： Appell方程 Chetaev 型约束力学系统 Lie对称性 守恒量     

约束Birkhoff系统的形式不变性

约束Birkhoff系统的形式不变性是约束Birkhoff方程在无限小变换下的一种不变性。给出约束Birkhoff系统形式不变性的定义与判据,并研究了这种形式不变性与Noether对称性之间的关系。     

Generalized energy integral and reduction of rotational relativistic Birkhoffian system

We study the order reduction method of the rotational relativistic Birkhoffian equations.For a rotational relativistic autonomous Birkhoffian system,if the conservative law of the Birkhoffian holds,the conservative quantity can be called the generalized energy integral.Through the eneralized energy integral,the order of the system can be reduced.If the rotational realtivistic Birkhoffian system has a generalized energy integral,then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the result.     

Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems

Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.     

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.     

Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.