共查询到18条相似文献,搜索用时 562 毫秒
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本文建立受匀速转动约束的变质量完整力学系统的运动微分方程,包括Lagrange形式的方程,Nielsen形式的方程和Appell形式的方程,并举例说明这些新型方程的应用。 相似文献
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变质量高阶非完整力学系统的运动微分方程 总被引:5,自引:0,他引:5
本文建立变质量力学系统的万有D'Alembert原理,由此导出变质量高阶非完整力学系统各种形式的运动微分方程,最后举例说明这些新型方程的应用. 相似文献
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Whittaker方程对非完整力学系统的推广 总被引:3,自引:0,他引:3
1904年Whittaker利用能量积分将一个完整保守力学系统问题降阶为一个带有较少自由度系统问题.并得到了Whittaker方程[1].本文推导对于非完整力学系统的这类方程.并称之为广义Whittaker方程;然后把这些方程变换为Nielsen形式;最后举例说明新方程的应用. 相似文献
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本文建立变质量非完整系统Routh形式的Kane方程,并由此导出变质量完整系统和非完整系统打击运动的Kane方程,其次指出Lagrange形式的打击运动方程与Kane方程的等价性。最后举例说明新方程的应用。 相似文献
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本文给出积分变质量非线性非完整系统相对于非惯性系动力学方程的梯度法,单分量法和场方法。首先,将这类问题的动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应常质量完整系统相对于惯性系的动力学方程,并加上非完整约束对初始条件的限制而得到变质量非线性非完整系统相对于非惯性系动力学方程的解。 相似文献
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变质量非线性非完整系统的Gibbs-Appell方程 总被引:1,自引:0,他引:1
本文首先将Gibbs-Appell方程推广到最一般的变质量非完整系统.得到变质量非线性非完整系统在广义坐标、准坐标下的Gibbs-Appell方程和积分变分原理,最后给出一个例子. 相似文献
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张毅 《数学物理学报(A辑)》2003,23(5):526-529
建立了相对论性Birkhoff系统的变分方程,并且利用系统的Birkhoff方程及其变分方程证明了可由第一积分直接构造该系统的一类积分不变量。文中举例说明了结果的应用。 相似文献
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转动系统的相对论性分析力学理论 总被引:20,自引:3,他引:17
本文讨论了转动相对论力学理论,主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Tr=∑ni=1I0iΓi2(1-1-θ·2i/Γi2)和广义加速度能量函数Sr=12∑ni=1Ii(θ·i·θ¨i)2Γi2-θ·2i+θ¨2i,给出其Hamilton原理和三种不同形式的D′Alembert原理;对于完整约束系统,建立了转动系统的相对论性Lagrange方程、Nielsen方程、Appel方程和Hamilton正则方程;对于非完整约束系统,建立了转动系统的相对论性Routh方程、Чаплыгин方程、Nielsen方程和Appel方程;并给出转动系统的相对论性Noether守恒律 相似文献
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本文将场方法推广应用于积分非完整可控力学系统的运动方程,并举例说明方法的应用. 相似文献
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R. Lávi?ka 《Complex Analysis and Operator Theory》2012,6(2):477-489
In this paper, we investigate properties of Gelfand–Tsetlin bases mainly for spherical monogenics, that is, for spinor valued
or Clifford algebra valued homogeneous solutions of the Dirac equation in the Euclidean space. Recently it has been observed
that in dimension 3 these bases form an Appell system. We show that Gelfand–Tsetlin bases of spherical monogenics form complete
orthogonal Appell systems in any dimension. Moreover, we study the corresponding Taylor series expansions for monogenic functions.
We obtain analogous results for spherical harmonics as well. 相似文献
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Vladislav V. Kravchenko Marco P. Ramirez T. 《Advances in Applied Clifford Algebras》2011,21(3):547-559
Considering one of the fundamental notions of Bers’ theory of pseudoanalytic functions the generating pair via an intertwining
relation we introduce its generalization for biquaternionic equations corresponding to different first-order systems of mathematical
physics with variable coefficients. We show that the knowledge of a generating set of solutions of a system allows one to
obtain its different form analogous to the complex equation describing pseudoanalytic functions of the second kind and opens
the way for new results and applications of pseudoanalytic function theory. As one of the examples the Maxwell system for
an inhomogeneous medium is considered, and as one of the consequences of the introduced approach we find a relation between
the time-dependent one-dimensional Maxwell system and hyperbolic pseudoanalytic functions and obtain an infinite system of
solutions of the Maxwell system. Other considered examples are the system describing force-free magnetic fields and the Dirac
system from relativistic quantum mechanics. 相似文献
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Hongjun Yu 《Journal of Differential Equations》2009,246(10):3776-3817
The relativistic Landau-Maxwell system is one of the most fundamental and complete models for describing the dynamics of a dilute hot plasma in which particles interact through Coulomb collisions and their self-consistent electromagnetic field. In this work, we prove that the classical solutions obtained by Strain and Guo become immediately smooth with respect to all variable under the extra assumption of the electromagnetic field. As a by-product, we also prove that the classical solutions to the relativistic Landau-Poisson system and the relativistic Landau equation have the same property without any extra assumption. 相似文献
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A new definition by means of a determinantal form for Appell (1880) [1] polynomials is given. General properties, some of them new, are proved by using elementary linear algebra tools. Finally classic and non-classic examples are considered and the coefficients, calculated by an ad hoc Mathematica code, for particular sequences of Appell polynomials are given. 相似文献
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《Mathematical and Computer Modelling》1996,23(3):103-128
The term of active structure is herein used (instead of variable structure) to emphasize that one deals with mechanical systems, some mechanical parameters of which (such as mass, inertia, rigidity) can be varied in time to account for environmental variations. One then has an internal structural control in addition to the usual external one in the form of forces or torques. By using a well-known classical result in physics, which characterizes a mechanical system by its Lagrangian only, one can obtain a new class of physically meaningful sliding equations for these systems. They are less severe regarding the mechanical constraints on the system, and they lower the amplitude of the chattering phenomenon. These systems can be controlled in a straightforward way by means of Barbashin-Utkin's variable structure technique. 相似文献
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A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a
linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties
of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either
torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration.
The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for
Fundamental Researches, Grant 02-01-00554. 相似文献