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A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 总被引:1,自引:0,他引:1 下载免费PDF全文
For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for t and qs, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables t, qs and qs. An example is given to illustrate the application of the results. 相似文献
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This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration. 相似文献
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Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems 下载免费PDF全文
For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of groups in which the generalized coordinates and time are variable. On the basis of the invariance of disturbed nonholonomic dynamical equations under general infinitesimal transformations, the determining equations, the constrained restriction equations and the additional restriction equations of Lie symmetries of the system are constructed, which only depend on the variables t, qs and q^.s. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for a nonholonomic system with the action of small disturbance is investigated, and the Lie symmetrical adiabatic invariants, the weakly Lie symmetrical adiabatic invariants and the strongly Lie symmetrical adiabatic invariants of generalized Hojman type of disturbed nonholonomic systems are obtained. An example is given to illustrate applications of the results. 相似文献
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A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type 总被引:5,自引:0,他引:5 下载免费PDF全文
For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t'or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results. 相似文献
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相对论非线性非完整系统动力学理论 总被引:19,自引:0,他引:19
本文提出了相对论分析力学的几个新型变分原理,建立了相对论力学的广义动能和广义加速度能的定义,导出了一阶非线性非完整系统的相对论性方程、Nielsen方程和Appell方程,并讨论了线性系、完整系和保守系的相对论性分析力学方程。 相似文献
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罗绍凯 《应用数学和力学(英文版)》1991,12(9):927-934
The new Lagrangian of the relative motion of mechanical system is constructed,thevariational principles of Jourdain’s form of nonlinear nonholonomic nonpotential system innoninertial reference frame are established,the generalized Noether’s theorem of thesystem above is presented and proved,and the conserved quantities of system are studied. 相似文献
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A FORM INVARIANCE OF CONSTRAINED BIRKHOFFIAN SYSTEM 总被引:2,自引:0,他引:2
IntroductionThestudyofthedynamicsofBirkhoffiansystemisanactivebranchinthemodernclassicalmathematicsandamoderndevelopingdirectioninmathematicphysics ,andcanbeappliedtoquantummechanics,statisticalmechanics ,biologicphysics,mechanicsofspaceflightandsomefie… 相似文献
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非完整约束系统几何动力学研究进展:Lagrange理论及其它 总被引:1,自引:1,他引:0
近10年来, 非完整力学的发展主要集中在两个相互关联的方向上, 一个是非完整运动规划, 另一个则是非完整约束系统的几何动力学, 这两个研究方向都充分地利用了现代几何学, 如纤维丛理论、辛流形和Poisson流形结构等等.本文主要综述非完整约束系统几何动力学的外附型和内禀型Lagrange理论, 包括非定常力学系统所需要的射丛几何学的基本概念、射丛按约束的直和分解、约束流形上的水平分布、D'Alembert-Lagrange方程与Chaplygin方程的整体描述、以及Riemann-Cartan流形上的非完整力学, 文中对Chetaev条件和d-δ交换关系的几何意义作了深入讨论.除此之外, 简要评述非完整力学的Hamilton理论与赝Poisson结构、Noether对称性和Lie对称性、动量映射与对称约化、Vakonomic动力学等几个非常重要专题的研究进展. 相似文献
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