广义Birkhoff系统的Birkhoff对称性与守恒量

研究广义Birkhoff系统的Birkhoff对称性问题,并给出此情形下相应的守恒量.将力学系统的等效Lagrange函数的一个定理推广到广义Birkhoff系统,证明了在一定条件下与两组动力学函数B,R_μ,Λ_μ和B,R_μ,Λ_μ分别给出的广义Birkhoff方程相关联的矩阵Λ 关键词： 广义Birkhoff系统 Birkhoff对称性 守恒量 矩阵迹     

Birkhoff系统的一类新型守恒量

给出了Birkhoff系统的一类新型守恒量。首先，建立了Birkhoff系统的运动方程及其Mei对称性的定义和判据；其次，给出了系统的一类新型守恒量的存在定理，并导出了用于确定无限小生成元的广义Killing方程；最后，建立了守恒定理的逆定理 关键词： Birkhoff系统 Mei对称性 守恒量 Killing方程     

Birkhoff系统的一类Lie对称性守恒量

给出了由Birkhoff系统的Lie对称性求守恒量的一种新方法.研究了系统仅依赖于Birkhoff变量a的Lie对称变换,直接由系统的Lie对称性得到了系统的一类守恒量,并举例说明结果的应用 关键词： 分析力学 对称性 守恒量 Birkhoff系统     

构造Birkhoff表示的Hojman方法与Birkhoff对称性

讨论了构造Birkhoff表示的Hojman方法.利用该方法重新研究Birkhoff对称性,提出一种关于该对称性的新见解,给出Birkhoff守恒量的新证明,并对该守恒量仅与Birkhoff张量相关作出解释.举例说明所得结果的应用.     

相对论Birkhoff系统的对称性与稳定性

讨论了相对论Birkhoff系统的三种对称性之间的关系，并利用Liapunov方法得到系统稳定性 的若干判据.随后，应用能量-Casimir函数法将系统稳定性与守恒量联系在了一起，并给出 了算例. 关键词： 相对论Birkhoff系统 对称性关系 稳定性 Liapunov方法 能量-Casimir函数     

单面约束Birkhoff系统的Noether理论

应用变换群G_r的无限小群变换的准对称性,给出了受单面约束的Brikhoff系统的Noether理论,并举例说明结果的应用. 关键词： 分析力学 单面约束Birkhoff系统 守恒量 对称性 Noether定理     

相对论性Birkhoff系统的Lie对称性和守恒量

给出相对论性Birkhoff系统的Pfaff-Birkhoff原理和Birkhoff方程.由微分方程在无限小变换下的不变性,定义相对论性Birkhoff系统无限小变换生成元,建立Lie对称的确定方程,得到结构方程和守恒量.并研究该系统的Lie对称性逆问题.给出实例以说明结果的应用. 关键词：     

广义Pfaff-Birkhoff-d'Alembert原理与广义Birkhoff系统的形式不变性

研究了广义Pfaff-Birkhoff-d'Alembert原理和广义Birkhoff系统在群的无限小变换下的形式不变性质.给出了形式不变性的判据,并由形式不变性导出Noether守恒量和新型守恒量.     

Rosenberg问题的对称性与守恒量

Rosenberg问题是一个典型而不太复杂的非完整系统问题.本文利用非完整系统的Noether对称性理论来求这个非完整力学问题的守恒量,进而得到问题的最终解.     

Lagrange系统形式不变性和Lutzky守恒量

研究Lagrange系统形式不变性导致的Lutzky守恒量．给出Lagrange系统形式不变性的判据，得到了系统的形式不变性是Lie对称性的充分必要条件．利用Lutzky的结论[6]证明了Lagrange系统形式不变性能导致Lutzky守恒量．举例说明结果的应用．     

Form invariance and new conserved quantity of generalised Birkhoffian system

A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. Firstly, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.     

Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relyingon the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.     

Hojman Conserved Quantities for Birkhoffian Systems in Event Space

This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry for a Birkhoffian system in the event space. The Birkhoffian parametric equations for the system are established, and the determining equations of Lie symmetry for the system are obtained. The conditions under which a Lie symmetry of Birkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojman conserved quantity are given. An example is given to illustrate the application of the results.     

Hojman Conserved Quantities for Birkhoffian Systems in Event Space

This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry for a Birkhoffian system in the event space. The Birkhoffian parametric equations for the system are established, and the determining equations of Lie symmetry for the system are obtained. The conditions under which a Lie symmetry of Birkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojman conserved quantity are given. An example is given to illustrate the application of the results.     

规范变换对Birkhoff系统对称性的影响

研究Birkhoff系统规范变换对其Noether对称性、Lie对称性和Mei对称性的影响.在一定条件下,Noether对称性和守恒量不改变.Lie对称性和Hojaman守恒量仍保持不变.Mei对称性和新型守恒量可能变化,得到了Mei对称性和新型守恒量保持不变的条件.举例说明结果的应用. 关键词： Birkhoff系统 规范变换 对称性 守恒量     

Noether Symmetry and Conserved Quantities of Fractional Birkhoffian System in Terms of Herglotz Variational Problem

The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional PfaffHerglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff's equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether's theorems within four different fractional derivatives are derived, which can reduce to the Noether's theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether's t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper.     

Symmetry and conserved quantities of discrete generalized Birkhoffian system

The Noether symmetry,the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper.Using the difference discrete variational approach,the difference discrete variational principle of discrete generalized Birkhoffian system is derived.The discrete equations of motion of the system are established.The criterion of Noether symmetry and Mei symmetry of the system is given.The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained.Finally,an example is given to show the applications of the results.     

变质量Birkhoff系统的Lie对称性和非Noether守恒量

采用嵌入质量法建立了变质量系统的Birkhoff方程.根据Lie对称性理论给出了变质量Birkhoff系统的Lie对称性确定方程，得到了系统的Lie对称直接导致非Noether守恒量的存在条件和形成.举例说明结果的应用. 关键词： 变质量 Birkhoff系统 Lie对称性 非Noether守恒量     

约束对Birkhoff系统Noether对称性和守恒量的影响

研究约束对Birkhoff系统的Noether对称性和守恒量的影响．首先，建立了Birkhoff系统的运动微分方程．其次，给出了系统Noether对称性的判据．然后，讨论了受约束作用后，Birkhoff系统的Noether对称性发生的变化，并给出了系统的Noether对称性以及守恒量保持不变的条件．最后，举例说明结果的应用． 关键词： 分析力学 Birkhoff系统 约束 Noether对称性 守恒量