共查询到20条相似文献,搜索用时 15 毫秒
1.
从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充.
关键词:
高阶速度能量
高阶Lagrange方程
高阶 Nielsen方程
高阶Appell方程 相似文献
2.
研究事件空间中力学系统的微分变分原理.基于D'Alembert原理,建立了事件空间中力学系统的D'Alembert-Lagrange原理、Jourdain原理、Gauss原理和万有D'Alembert原理,给出了这些原理的Euler-Lagrange参数形式、Nielsen参数形式和Appell参数形式,并导出了万有D'Alembert原理的Mangeron-Deleanu参数形式.
关键词:
分析力学
事件空间
微分变分原理 相似文献
3.
从Мещерский方程出发,建立变质量力学系统的高阶D'Alembert-Lagrange原理,导出变质量完整力学系统的各类高阶运动微分方程.结果表明,它们扩充和优化了完整力学的相关理论.
关键词:
变质量完整力学系统
高阶力变率
高阶D'Alembert-Lagrange原理
高阶运动微分方程 相似文献
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研究事件空间中Birkhoff系统动力学.在(2n+1)维事件空间中,建立了Birkhoff系统的Pfaff-Birkhoff-d'Alembert原理和Birkhoff参数方程,研究了方程的第一积分,给出了第一积分及其存在条件.
关键词:
Birkhoff系统
事件空间
参数方程
第一积分 相似文献
7.
从质点系非惯性系的动力学方程出发,建立力学系统相对运动的高阶微分变分原理,然后引入力学系统的高阶相对速度能量,导出完整力学系统相对运动的各类高阶动力学方程,并给出一例说明本文结果的应用.
关键词:
完整力学系统
相对运动
高阶微分变分原理
高阶动力学方程 相似文献
8.
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle. 相似文献
9.
Higher-order implicit strong numerical schemes for stochastic differential equations 总被引:2,自引:0,他引:2
Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined. 相似文献
10.
Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space 下载免费PDF全文
This paper is devoted to studying the conformal invariance
and Noether symmetry and Lie symmetry of a holonomic mechanical
system in event space. The definition of the conformal invariance
and the corresponding conformal factors of the holonomic system in
event space are given. By investigating the relation between the
conformal invariance and the Noether symmetry and the Lie symmetry,
expressions of conformal factors of the system under these
circumstances are obtained, and the Noether conserved quantity and
the Hojman conserved quantity directly derived from the conformal
invariance are given. Two examples are given to illustrate the
application of the results. 相似文献
11.
In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented. 相似文献
12.
研究事件空间中完整力学系统Lie对称性的摄动与绝热不变量.基于力学系统的高阶绝热不变量的概念,研究在小扰动作用下系统Lie对称性的摄动,得到了事件空间中完整力学系统的一类Hojman形式的高阶绝热不变量,给出了绝热不变量存在的条件及形式.并举例说明结果的应用.
关键词:
事件空间
对称性
摄动
绝热不变量 相似文献
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研究事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到由Mei对称性直接导致的Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结果的应用.
关键词:
事件空间
Nielsen方程
单面非Chetaev型非完整系统
Mei守恒量 相似文献
15.
For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coordinates for the system is given and the corresponding cyclic integral is obtained. Through the cyclic integral, the order of the system can be reduced. The Routh functions for the Birkhoffian system in the event space are constructed, and the Routh method of reduction is successfully generalized to the Birkhoffian system in the event space. The results show that if the system has a cyclic integral, then the parametric equations of the system can be reduced at least by two degrees and the form of the equations holds. An example is given to illustrate the application of the results. 相似文献
16.
<正>This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space.The Birkhoff's equations in the event space are given.The Poisson theory of the Birkhoffian system in the event space is established.The definition of the Jacobi last multiplier of the system is given,and the relation between the Jacobi last multiplier and the first integrals of the system is discussed.The researches show that for a Birkhoffian system in the event space,whose configuration is determined by(2n + 1) Birkhoff's variables,the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known.An example is given to illustrate the application of the results. 相似文献
17.
By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance. 相似文献
18.
Francesco Calogero 《Journal of Nonlinear Mathematical Physics》2017,24(1):142-148
A technique to identify new C-integrable and S-integrable systems of nonlinear partial differential equations is reported, with two representative examples displayed and tersely discussed. 相似文献
19.
Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential
evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution
equations were lifted to the corresponding functional partial differential equations in functional space by introducing the
time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The
algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact
analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution
equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer
numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic
dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution
equations both analytically and numerically.
Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program
Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China 相似文献
20.
Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space 下载免费PDF全文
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. 相似文献