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We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed.  相似文献   

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Given a bounded open subset of R n, we prove the existence of a minimum point for a functional F defined on the family A() of all quasiopen subsets of , under the assumption that F is decreasing with respect to set inclusion and that F is lower semicontinuous on A() with respect to a suitable topology, related to the resolvents of the Laplace operator with Dirichlet boundary condition. Applications are given to the existence of sets of prescribed volume with minimal k th eigenvalue (or with minimal capacity) with respect to a given elliptic operator.  相似文献   

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This paper introduces a general iterative algorithm to approximate a common element in the solution set of quasi-variational inclusion problems and the common fixed point set of an infinite family of nonexpansive mappings. It is proven that the iterative sequences generated in the proposed iterative algorithm converge strongly to some common element in the framework of the real Hilbert spaces.  相似文献   

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A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton–Jacobi–Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).  相似文献   

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Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X, define S: X → X by Sx =f−Tx+x, for all x ε X. Let {an} n=0 , {βn} n=0 be two real sequences in (0, 1) satisfying:
((i))
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((ii))
Assume that {un} n=0 and {υn} n=0 are two sequences in X satisfying ‖un‖ = 0(αn) and ‖υn‖ → 0 as n → ∞. For arbitrary x0 ε X, the iteration sequence {xn} is defined by
(1)
Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S.  相似文献   

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A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.  相似文献   

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The perturbed rotational motion of a gyrostat about a fixed point with mass distribution near to Lagrange’s case is investigated. The gyrostat is subjected under the influence of a variable restoring moment vector, a perturbing moment vector, and a third component of a gyrostatic moment vector. It is assumed that the angular velocity of the gyrostat is sufficiently large, its direction is close to the axis of dynamic symmetry, and the perturbing moments are small as compared to the restoring ones. These assumptions permit us to introduce a small parameter. Averaged systems of the equations of motion in the first and second approximations are obtained. Also, the evolution of the precession angle up to the second approximation is determined. The graphical representations of the nutation and precession angles are presented to describe the motion at any time.  相似文献   

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A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.  相似文献   

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A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.  相似文献   

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The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich(Ekonomika i Matematicheskie Metody,1976,12(4):747-756),but also extend and replenish the corresponding results obtained by Iiduka and Takahashi(Nonlinear Anal TMA,2005,61(3):341-350),Takahashi and Toyoda(J Optim Theory Appl,2003, 118(2):417-428),Nadezhkina and Takahashi(J Optim Theory Appl,2006,128(1):191- 201),and Zeng and Yao(Taiwanese Journal of Mathematics,2006,10(5):1293-1303).  相似文献   

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In this paper,a class of singularly perturbed initial-boundary value problems for thereaction diffusion systems is considered.Using the theory of differential inequality,weprove that the initial-boundary value problems have a solution and obtain their asymptoticexpansion.  相似文献   

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叙述刚体动力学中Serret-Andoyer变量的基本概念. 导出用其表达的刚体定点运动动力学方程,叙述其在航天器姿态动力学和陀螺力学中的应用.  相似文献   

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研究在给定材料体积的条件下绕定轴旋转的平板结构的拓扑优化设计,以使受到冲击荷载后平板结构的振动最小,采用积分形式的二次型性能指标为目标函数,以单元人工密度为设计变量建立拓扑优化列式.假定板结构在面内以常速旋转并考虑小应变假设,采用多体动力学理论和有限元方法建立运动微分方程.使用李亚普洛夫第二方法将积分形式的二次型性能指...  相似文献   

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