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1.
In this paper we study the Lagrangian reduction of generalized nonholonomic systems (GNHS) with symmetry. We restrict ourselves to those GNHS, defined on a configuration space Q, with kinematic constraints given by a general submanifold CK⊂TQ, and variational constraints given by a distribution CV on Q. We develop a reduction procedure that is similar to that for nonholonomic systems satisfying d’Alembert’s principle, i.e. with CK a distribution and CV=CK. Special care is taken in identifying the geometrical structures and mappings involved. We illustrate the general theory with an example. 相似文献
2.
就一般非完整约束系统,从约束方程满足的变分恒等式出发,利用增广位形流形上的向量场定义三类非自由变分,即非完整变分:vakonomic变分、Hlder变分、Suslov变分,并讨论它们之间的关系以及它们成为自由变分的充要条件.利用非完整变分以及相应的积分变分原理建立两类动力学方程:vakonomic方程和Routh方程或Chaplygin方程.通过vakonomic方程分别与Routh方程和Chaplygin方程比较,得到它们具有共同解的两类充分必要条件.这些条件并不是约束的可积性条件.
关键词:
非完整约束
非完整变分
Chetaev条件
vakonomic动力学 相似文献
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The Lie-form invariance of a nonholonomic mechanical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechanical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is given to illustrate the application of the results. 相似文献
5.
The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is estab- lished, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal trans- formations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results. 相似文献
6.
By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether's theorem and the Noether's inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result. 相似文献
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The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results. 相似文献
9.
This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert–Lagrange principle with fractional derivatives is presented,and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results. 相似文献
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This paper constructs an almost-Poisson structure for the
non-self-adjoint dynamical systems, which can be decomposed into a
sum of a Poisson bracket and the other almost-Poisson bracket. The
necessary and sufficient condition for the decomposition of the
almost-Poisson bracket to be two Poisson ones is obtained. As an
application, the almost-Poisson structure for generalised
Chaplygin's systems is discussed in the framework of the
decomposition theory. It proves that the almost-Poisson bracket for
the systems can be decomposed into the sum of a canonical Poisson
bracket and another two noncanonical Poisson brackets in some special
cases, which is useful for integrating the equations of motion. 相似文献
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Based on the weak Noether symmetry proposed by Mei F X, this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type, and presents expressions of three kinds of conserved quantities by weak Noether symmetry. Finally, the application of this new results is showed by a practical example. 相似文献
14.
A new model in nonholonomic mechanics,the Rosen--Edelstein model, has been
studied. We prove that the new model is a Lagrange problem in which the action
integral $\int^{t_{1}}_{t_{0}}L\dd t$ can be made stationary.The theoretical basis
of nonholonomic mechanics is investigated and discussed. Finally, we give the range
of practical applications of theRosen--Edelstein model. 相似文献
15.
Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results. 相似文献
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Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm 下载免费PDF全文
By using the discrete variational method, we study the numerical method of the general nonholonomic system in the generalized Birkhoffian framework, and construct a numerical method of generalized Birkhoffian equations called a self-adjoint-preserving algorithm. Numerical results show that it is reasonable to study the nonholonomic system by the structure-preserving algorithm in the generalized Birkhoffian framework. 相似文献
18.
In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations. 相似文献
19.
研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整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的形式,并举例说明结果的应用.
关键词:
相空间
二阶线性非完整系统
形式不变性
守恒量 相似文献