共查询到18条相似文献,搜索用时 140 毫秒
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根据Cosserat弹性杆的动力学普遍定理,讨论其守恒量问题. 因弹性杆的动力学方程是以截面为对象,并且是以弧坐标和时间为双自变量,其守恒量必定是以积分的形式给出,分别存在关于弧坐标或时间守恒的问题. 根据弹性杆的动量和动量矩方程,导出其动量守恒和动量矩守恒的存在条件及其表达,并讨论了关于沿中心线弧坐标的守恒问题;再分别根据弹性杆关于时间和弧坐标的能量方程导出了各自的关于时间和弧坐标的守恒量存在条件及其表达, 结果包括了弹性杆的机械能守恒以及平衡时的应变能积分;守恒问题给出了例子. 积分形式的守恒量对于弹性杆动力学的理论分析和数值计算都具有实际意义.
关键词:
守恒量
Cosserat弹性杆
动力学普遍定理
双自变量 相似文献
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由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程. 相似文献
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依据定量因果原理的数学表示,统一地导出了Lagrange量中含坐标关于时间一阶、二阶导数 的积分型的Hamilton原理、Voss原理、Hlder原理和Maupertuis-Lagrange原理等,给出了 这些原理的本质联系和统一描述.得出f0=0并不是通常的保持Euler-Lagrange方 程不 变的结果,而是满足定量因果原理的结果.还得出Lagrange量的所有的积分型变分原理等价 地对应于两类满足定量因果原理的不变形式.同时发现所有积分型变分原理的运动方程都是E uler-Lagrange 方程,但不同条件的变分原理所对应的不同群G作用下的守恒量是不同 的.从而可对过去众多零散的积分型变分原理有一个系统和深入的理解,并使这些变分原理 自然地成为定量因果原理的推论.
关键词:
变分原理
因果原理
运动方程
对称性 相似文献
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研究Lagrange系统的Mei对称性直接导致的一种守恒量. 给出系统的Mei对称性的定义和判据方程, 得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用.
关键词:
Lagrange系统
Mei对称性
守恒量 相似文献
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In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
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In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
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In this paper the conservation theorems of the constrained Birkhoffian systems are
studied by using the method of integrating factors. The differential equations of
motion of the system are written. The definition of integrating factors is given
for the system. The necessary conditions for the existence of the conserved quantity
for the system are studied. The conservation theorem and its inverse for the system
are established. Finally, an example is given to illustrate the application of the
results. 相似文献
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In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results. 相似文献
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Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics 总被引:1,自引:0,他引:1
QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(1):43-45
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
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QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(7)
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
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The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied.First,the dynamical equations of relative motion of system are written.Next,the definition of integrating factors is given,and the necessary conditions for the existence of the conserved quantities are studied in detail.Then,the conservation theorem and its inverse of system are established.Finally,an example is given to illustrate the application of the result. 相似文献