共查询到19条相似文献,搜索用时 125 毫秒
1.
相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量 总被引:4,自引:0,他引:4
研究相空间中有二阶线性单面约束的非完整系统的Lie对称性与守恒量。首先根据微分方程在无限小变换下的不变性建立Lie对称性所满足的确定方程和限制方程,给出结构方程和守恒量;其次讨论系统的Lie对称性逆问题。最后举一实例说明结果的应用。 相似文献
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为了进一步揭示非完整系统的对称性和守恒量之间的内在关系,提出并研究基于分数阶模型的非完整系统的Mei对称性及其守恒量.首先,根据分数阶d’Alembert-Lagrange原理建立基于分数阶模型的非完整系统的动力学方程.其次,根据动力学方程中的动力学函数经无限小变换后仍满足原方程的不变性,建立分数阶模型下非完整系统的Mei对称性定理,给出Mei守恒量.再次,讨论了几个特例:分数阶Hamilton系统、经典非完整系统和受非完整约束的分数阶Lagrange系统的Mei对称性定理.文末举例说明结果的应用. 相似文献
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将对称性分为Noether对称性、Lie对称性和形式不变性等3种类型,将守恒量分为Noether守恒量、Hojman守恒量和新型守恒量等3种类型.研究Lagrange系统同一类型对称性生成不同类型守恒量的问题. 相似文献
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将非力学系统的微分方程化成Hamilton方程形式,引进无限小变换,研究微分方程或Hamilton作用量在无限小变换下的不变性,进而给出守恒量存在的条件以及守恒量的形式. 相似文献
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将非力学系统的微分方程化成Hamilton方程形式,引进无限小变换,研究微分方程或Hamilton作用量在无限小变换下的不变性,进而给出守恒量存在的条件以及守恒量的形式。 相似文献
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将非力学系统的微分万程化成Lagrange方程形式,引进无限小变换,研究微分方程或Hamilton作用量在无限小变换下的不变性,进而给出守恒星存在的条件以及守恒量的形式. 相似文献
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将非力学系统的微分方程化成Lagrange方程形式,引进无限小变换,研究微分方程或Hamilton作用量在无小变换,研究微分方程或Hamilton作用量在无限小变换下的不变性,进而给出守恒量存在的条件以及守恒量的形式。 相似文献
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将非力学系统的微分方程化成Hamilton方程形式,引进无限小变换, 研究微分方程或Hamilton作用量在无限小变换下的不变性, 进而给出守恒量存在的条件以及守恒量的形式. 相似文献
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具有可积微分约束的力学系统的Lie对称性 总被引:7,自引:0,他引:7
研究具有可积微分约束的力学系统的Lie对称性与守恒量。采用两种方法:一是用不可积微分约束系统的方法;另一是用积分后降阶系统的方法,研究两种方法之间的关系。 相似文献
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对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统. 由于完整力学系统的第二类Lagrange 方程中没有约束力,故为研究完整力学系统的约束力,需采用有多余坐标的带乘子的Lagrange方程或第一类Lagrange 方程. 一些动力学问题要求约束力不能为零,而另一些问题要求约束力很小. 如果约束力为零,则称为系统的自由运动问题. 本文提出并研究了有多余坐标完整系统的自由运动问题. 为研究系统的自由运动,首先,由d'Alembert-Lagrange 原理, 利用Lagrange 乘子法建立有多余坐标完整系统的运动微分方程;其次,由多余坐标完整系统的运动方程和约束方程建立乘子满足的代数方程并得到约束力的表达式;最后,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件. 这些条件的个数等于约束方程的个数,它们依赖于系统的动能、广义力和约束方程,给出其中任意两个条件,均可以得到实现自由运动时对另一个条件的限制. 即当给定动能和约束方程,这些条件会给出实现自由运动时广义力之间的关系. 当给定动能和广义力,这些条件会给出实现自由运动时对约束方程的限制. 当给定广义力和约束方程,这些条件会给出实现自由运动时对动能的限制. 文末,举例并说明方法和结果的应用. 相似文献
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The conformal invariance and conserved quantity for the nonholonomic system of non-Chetaev’s type are studied. Firstly, by
introducing a one-parameter infinitesimal transformation group and its infinitesimal generator vector, the definition of conformal
invariance and determining equation for the holonomic system which corresponds to a nonholonomic system of non-Chetaev’s type
are provided, and the relationship between the system’s conformal invariance and Lie symmetry are discussed. Secondly, the
conformal invariance of weak and strong Lie symmetry for the nonholonomic system of non-Chetaev’s type is given using restriction
equations and additional restriction equations. Thirdly, the system’s corresponding conserved quantity is derived with the
aid of a structure equation that the gauge function satisfies. Lastly, an example is given to illustrate the application of
the method and its result. 相似文献
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The form invariance and the conserved quantity for a weakly nonholonomic system (WNS) are studied. The WNS is a nonholonomic system (NS) whose constraint equations contain a small parameter. The differential equations of motion of the system are established. The definition and the criterion of form invariance of the system are given. The conserved quantity deduced from the form invariance is obtained. Finally, an illustrative example is shown. 相似文献
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IntroductionIn1979,R.BengtssonandS.Franendorfaccuratlymeasuredthemaximumvaluesofthespinvelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvalueofthespinvelocityofonenucleonwasdifferenttothoseoftheothers[1].Withthedevelopmentofscienceandtechnology,… 相似文献
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For a weakly nonholonomic system, the Lie symmetry and approximate Hojman conserved quantity of Appell equations are studied. Based on the Appell equations for a weakly nonholonomic system under special infinitesimal transformations of a group in which the time is invariable, the definition of the Lie symmetry of the weakly nonholonomic system and its first-degree approximate holonomic system are given. With the aid of the structure equation that the gauge function satisfies, the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are derived. Finally, an example is given to study the exact and approximate Hojman conserved quantity of the system. 相似文献
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梅凤翔 《应用数学和力学(英文版)》1999,20(6):629-634
In this paper, the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied. By using
the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations and
the conserved quantities are given. And an example is given to illustrate the application of the result.
Foundation item: the National Natural Science Foundation of China (19572038) 相似文献
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For a nonholonomic system of Chetaev’s type, the conformal invariance and the conserved quantity of Mei symmetry for Appell equations are investigated. First, under the infinitesimal one-parameter transformations of group and the infinitesimal generator vectors, Mei symmetry and conformal invariance of differential equations of motion for the system are defined, and the determining equation of Mei symmetry and conformal invariance for the system are given. Then, by means of the structure equation to which the gauge function is satisfied, the Mei-conserved quantity corresponding to the system is derived. Finally, an example is given to illustrate the application of the result. 相似文献
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Form invariance and noether symmetrical conserved quantity of relativistic Birkhoffian systems 总被引:1,自引:0,他引:1
罗绍凯 《应用数学和力学(英文版)》2003,24(4):468-478
IntroductionIn 1 92 7,theAmericanmathematicianG .D .BirkhoffmadeprimaryresearchesonBirkhoffiandynamics[1].In 1 983,theAmericanphysicistR .M .SantillistudiedthetransformationtheoryofBirkhoffequationsandgeneralizationofGalileirelativity ,andsummarizedcomprehensivelytheoriginofBirkhoffequationsandthelaterstudiesonthem[2 ].Since 1 992 ,theChinesemechanicianMeiFeng_xianganditsco_workershaveconstructedthedynamicsofBirkhoffiansystemonthebasisofRefs.[1 ,2 ] ,andgavethebasictheoreticalframe[3 - … 相似文献