转动系统相对论性Birkhoff动力学的基本理论

建立转动系统相对论性Birkhoff动力学的基本理论,给出其Birkhoff函数和Birkhoff函数组、Pfaff作用量、Pfaff-Birkhoff原理、Pfaff-Birkhoff-D’Alembert原理,以及Birkhoff方程.并研究转动系统相对论性Lagrange力学、Hamilton力学与转动系统相对论性Birkhoff动力学之间的关系,证明完整保守、完整非保守转动相对论系统都可纳入转动相对论Birkhoff系统 关键词： 转动系统 相对论 Birkhoff动力学 变分原理     

转动相对论Birkhoff约束系统积分不变量的构造

研究转动相对论Birkhoff约束系统积分不变量的构造首先,建立转动相对论系统的约束Birkhoff方程;其次,利用等时变分与非等时变分之间的关系建立系统的非等时变分方程;然后,研究转动相对论Birkhoff约束系统的第一积分与积分不变量之间的关系,证明由系统的一个第一积分可以构造一个积分不变量,并给出自由Birkhoff系统的相应结果;最后,讨论转动相对论Hamilton系统、相对论Birkhoff系统和Hamilton系统、经典转动系统和等时变分情形下的积分不变量的构造,结果表明相关的结论均为该定理的特款给出一个例子说明结果的应用 关键词： 转动相对论 Birkhoff系统 约束 第一积分 积分不变量     

A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System

A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.     

相对论Birkhoff系统动力学研究

给出相对论系统的Birkhoff函数和Birkhoff函数组、Pfaff作用量、PfaffBirkhoff原理、Birkhoff方程;研究相对论动力学系统的Birkhoff表示方法;根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;研究相对论Birkhoff系统的代数结构和Poisson积分方法. 关键词： 相对论 Birkhoff系统 Noether对称性 Lie对称性 代数结构 Poisson积分     

A Geometrical Approach to Hojman Theorem of a Rotational Relativistic Birkhoffian System

A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.     

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.     

转动系统的相对论性分析静力学理论

建立转动系统的相对论性分析静力学理论，给出转动系统的相对论性虚功原理、转动系统的相对论性广义平衡方程以及转动系统的相对论性有势系广义平衡方程. 关键词： 转动系统 相对论 分析静力学     

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.     

转动相对论系统的Appell方程及其形式不变性

给出转动相对论系统的Appell方程,讨论相对论力学的四个新型基本动力学函数 在无限小群变换下研究转动相对论系统Appell方程的形式不变性,给出定义和判据 研究形式不变性与Noether对称性与Lie对称性的关系,寻求转动相对论系统的守恒量 关键词： 转动相对论 Appell方程 形式不变性 对称性与守恒量     

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.     

相对论性转动变质量系统的Lie对称性与守恒量

给出相对论性转动变质量系统的d’Alembert原理和运动微分方程.利用运动微分方程在无限小变换下的不变性,建立相对论性转动变质量系统的Lie对称确定方程,得到结构方程和守恒量.并举例说明结果的应用 关键词： 相对论 转动 变质量 Lie对称     

转动相对论Birkhoff系统的平衡稳定性

研究转动相对论Birkhoff系统的平衡稳定性，给出转动相对论Birkhoff自治系统、半自治系统和非自治系统的平衡方程和转动相对论Birkhoff自治系统的受扰运动方程和一次近似方程；给出转动相对论Birkhoff自治系统平衡稳定性的一次近似方法及其判据；并给出转动相对论Birkhoff自治系统平衡稳定性的直接方法及其判据；讨论转动相对论Birkhoff系统平衡稳定性和经典转动Birkhoff系统平衡稳定性的关系.给出实例以说明方法的应用. 关键词： 相对论 转动Birkhoff系统 平衡稳定性 一次近似方法     

A Set of Lie Symmetrical Conservation Law for Rotational Relativistic Hamiltonian Systems

For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determining equations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.     

Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D‘Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.     

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.     

非完整转动相对论系统的Lindel?f方程

由转动相对论系统的Hamilton原理分别建立在广义坐标和准坐标下的Lindel?f方程及其改进形式,并从改进的Lindel?f方程导出新Chaplygin方程.最后说明由转动系统的相对论分析力学向普通分析力学过渡的方法. 关键词： 非完整约束 转动系统 相对论 Lindel?f方程 Chaplygin方程     

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.     

Noether‘s theorem of a rotational relativistic variable mass system

Noether‘s theory of a rotational relativistic variable mass system is studied.Firstly,Jourdain‘s principle of the rotational relativistic variable mass system is given.Secondly,on the basis of the invariance of the Jourdain‘s principle under the infinitesimal transformations of groups,Noether‘s theorem and its inverse theorem of the rotational relativistic variable mass system are presented.Finally,an example is given to illustrate the application of the result.     

A Set of Lie Symmetrical Conservation Law for Rotational Relativistic Hamiltonian Systems

For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantitiesare given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, andintroducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determiningequations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example isgiven to illustrate the application of the results.     

Poisson theory and integration method of Birkhoffian systems in the event space

<正>This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space.The Birkhoff's equations in the event space are given.The Poisson theory of the Birkhoffian system in the event space is established.The definition of the Jacobi last multiplier of the system is given,and the relation between the Jacobi last multiplier and the first integrals of the system is discussed.The researches show that for a Birkhoffian system in the event space,whose configuration is determined by(2n + 1) Birkhoff's variables,the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known.An example is given to illustrate the application of the results.