相空间中非完整非保守系统的形式不变性

研究相空间中非完整非保守系统的形式不变性.给出相空间中非完整非保守系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量形式，并举例说明结果的应用. 关键词： 相空间 非完整非保守系统 形式不变性     

非完整系统的形式不变性与Hojman守恒量

研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下，给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程，提出并定义弱（强）形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件，由系统的特殊形式不变性，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出两个经典例子说明结果的应用. 关键词： 分析力学 非完整系统 形式不变性 非Noether守恒量 Hojman守恒量     

非完整系统Hamilton正则方程的形式不变性

研究非完整系统Hamilton正则方程的形式不变性，给出形式不变性的定义和判据，建立形式不变性和系统守恒量之间的关系，并举例说明结果的应用. 关键词： 非完整系统 Hamilton正则方程 形式不变性 守恒量     

非Chetaev型非完整可控力学系统的Noether-形式不变性

基于函数对时间的全导数采用沿系统的运动轨线方式, 研究非Chetaev型非完整可控力学系统的Noether-形式不变性. 给出非Chetaev型非完整可控力学系统的Noether-形式不变性的定义和判据. 由Noether-形式不变性同时得到了Noether守恒量和新型守恒量. 并举例说明结果的应用. 关键词： 非Chetaev型非完整系统 可控力学系统 Noether-形式不变性 守恒量     

相对论性变质量非完整可控力学系统的非Noether守恒量

在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn守恒量.建立了系统的运动微分方程, 给出了系统在特殊无限小变换下的形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非Noether守恒量的条件和具体形式.举例说明结果的应用. 关键词： 相对论 非完整可控力学系统 变质量 非Noether守恒量     

完整力学系统的Lie-形式不变性

研究完整力学系统Lie-形式不变性的定义与判据，给出由Lie-形式不变性导出的Noether守恒量，Hojman守恒量和Lutzky守恒量. 举例说明结果的应用. 关键词： 完整系统 Lie-形式不变性 Noether守恒量 Hojman守恒量 Lutzky守恒量     

相空间中非完整可控力学系统的对称性摄动与绝热不变量

研究相空间中非完整可控力学系统的对称性摄动与绝热不变量. 列出相空间中未受扰非完整可控力学系统的形式不变性导致的Noether守恒量. 基于力学系统高阶绝热不变量的定义，研究小扰动作用下相空间中非完整可控力学系统的形式不变性摄动与绝热不变量，给出了精确不变量与绝热不变量存在的条件与形式，并举例说明结果的应用.     

非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量

研究非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量.列出系统的Raitzin正则方程.提出在无限小变换下系统形式不变性的定义和判据.给出系统的形式不变性是Lie对称性的充要条件.建立Hojman守恒定理，并举例说明结果的应用. 关键词： 非保守系统 Raitzin正则方程 形式不变性 非Noether守恒量     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量     

包含伺服约束的非完整系统的Lie对称性与守恒量

利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式. 关键词： 非完整系统 伺服约束 Lie对称性 守恒量     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of 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.     

Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system

A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.     

Form invariance and conserved quantities of Nielsen equations of relativistic variable mass nonholonomic systems

In this paper, the definition and criterion of the form invariance of Nielsen equations for relativistic variable mass nonholonomic systems are given. The relation between the form invariance and the Noether symmetry is studied.Finally, we give an example to illustrate the application of the result.     

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.     

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.