The integration methods of Vacco dynamics equation of nonlinear nonholonomic system

ＴＨＥＩＮＴＥＧＲＡＴＩＯＮＭＥＴＨＯＤＳＯＦＶＡＣＣＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＯＦＮＯＮＬＩＮＥＡＲＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＬｕｏＳｈａｏｋａｉ（罗绍凯）（ＲｃｅｅｉｖｅｄＡｕｇ．２．１９９３：ｃｏｍｍｕｎｉｃａｔｅｄｂｙＷａｎ...     

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results.     

Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space

Hojman conserved quantities deduced from the special Lie symmetry, the Noether symmetry and the form invariance for a nonholonomic system of the unilateral non-Chetaev type in the event space are investigated. The differential equations of motion of the system above are established. The criteria of the Lie symmetry, the Noether symmetry and the form invariance are given and the relations between them are obtained. The Hojman conserved quantities are gained by which the Hojman theorem is extended and applied to the nonholonomic system of the unilateral non-Chetaev type in the event space. An example is given to illustrate the application of the results.     

Theory of symmetry for a rotational relativistic Birkhoff system

The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff－Birkhoff－D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given.     

Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.     

A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

For a rotational relativistic Birkhoffian system a set of the Lie symmetries and conservation laws is given under infinitesimal transformation. On the basis of the invariance of rotational relativistic Birkhoffian equations under infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetries are given, and a new type of non-noether conserved quantities are directly obtained from Lie symmetries of the system. An example given to illustrate the application of the results.     

Stability for the equilibrium state manifold of relativistic Birkhoffian systems

In this paper, the stability of equilibrium state manifold for relativistic Birkhoffian systems in studied. The equilibrium state equations, the disturbance equations and their first approximation are presented. The criteria of stability for the equilibrium state manifold are obtained. The relationship between the stability of the equilibrium-state manifold of relativistic Birkhoffian systems and that of classical Birkhoffian systems is discussed. An example is given to illustrate the results.     

Lagrange-Maxwell系统的Lie对称性与守恒量

由微分方程在无限小主为换下的不变性,定义Ｌａｇｒａｎｇｅ－Ｍａｘｗｅｌｌ方程元限元小变失生成元,给出Ｌｉｅ对称性的确定方程,得到结构方程和守恒量。     

变质量非完整系统相对运动动力学方程的积分理论

本文研究变质量非线性非完整系统相对于非惯性系动力学的积分理论，给出其Ｒｏｕｔｈ降阶法，Ｗｈｉｔｔａｋｅｒ降阶法，Ｐｏｉｎｃａｒｅ－Ｃａｒｔａｎ型积分变量关系和积分不变量。