Control of the rotational motion of the rigid body with the help of internal rotors using Rodrigues-Caley parameters

The purpose of this paper is to study the control of the rotational motion of the rigid body with the help of three rotors attached to the principal axes of the body. In such study the asymptotic stability of this motion is proved by using the Lyapunov technique. As a particular case of our problem, the equilibrium position of the rigid body, which occurs when the principal axes of inertia of the body coincide with the inertial axes, is proved to be asymptotically stable. The control moments that impose the stabilization of the rotational motion and equilibrium position are obtained.     

Self-induced jumping of a rigid body of revolution on a smooth horizontal surface

The article is devoted to the study of the motion of a rigid body of revolution on a rigid and perfectly smooth horizontal surface under the influence of the uniform gravitational field. Basic equations are listed and their solutions are given. The unilateral contact between the body and the plane at non-steady motion is investigated and the procedure of calculation of threshold values of the body energy above which the contact is broken is given. In contrast to Shimomura et al. [Dynamics of an axisymmetric body spinning on a horizontal surface. II. Self-induced jumping. Proc. R. Soc. A 461 (2005) 1775-1809], who assumed sliding friction in their analysis, it is found that the self-induced jumping can also occur in the absence of friction at the very beginning of the motion. The free motion after the contact is lost and impact of the body when it again makes contact with the plane is discussed. The motion of a spheroid and a disk which illustrate the results of the general theory are discussed in some detail.     

Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.     

A hybrid scheme for simulation of planar rigid bodies with impacts and friction using impact mappings

This paper introduces numerical techniques necessary for the implementation of impact maps derived from an energetic impact law for rigid-body impacts with friction at isolated contact points. In particular the work focuses on methodologies for long-term simulation with behaviours such as dynamic transitions and chatter. The methods are based on hybrid event-driven numerical solvers for ordinary differential equations together with system states to deal with the transitions. A slender rod impacting a periodically oscillating surface is used as an example to illustrate implementation and methods. The numerical scheme for the rod system is used to show how symmetry can play an important role in the presence of friction for long-term dynamics. This will show that surface oscillations with low frequencies tend to lead to periodic motions of the rod that are independent of friction. For higher frequencies however the periodic solutions are not that common and irregular motion ensues.     

New solvable problems in the dynamics of a rigid body about a fixed point in a potential field

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.     

猎雷声纳基阵姿态稳定系统自适应反步法控制

针对带非线性摩擦力矩和负载扰动的高精度猎雷声纳基阵姿态稳定系统,提出了一种基于神经网络的自适应反步法控制方法。其中神经网络用于估计未知非线性摩擦力矩,进而设计反步法控制器和参数自适应律来对神经网络估计误差和负载扰动进行补偿。最后应用Lyapunov方法证明了所提出的自适应控制器能保证闭环系统的稳定性,并且可以通过选择适当的控制器参数来调整收敛率。仿真结果表明,基于神经网络的自适应反步法控制方法与PID控制相比,系统的动、静态性能指标及鲁棒性得到了全面的改善,与双闭环PID控制相比,跟踪精度提高了3倍多。     

Attitude stabilization of the rotational axis of a carrying body by pendulum dampers

The paper addresses attitude stabilization of the rotational axis of an asymmetric carrying body by pendulum dampers. Steady motions in which the kinetic energy of the system takes stationary values are identified. Whether these motions are stable is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 120–128, October 2007.     

一类刚-梁耦合系统平面稳态运动的稳定性

研究了中心力场中的一类刚-弹耦合系统的平面运动动力学，模型是带有一悬臂 梁的刚体. 综合考虑了系统轨道运动与姿态运动，在Lagrange力学体系下给出了系统的运 动方程，在保守系统和考虑梁的材料黏滞阻尼两种情况下，利用能量-动量方法给出了一类 相对平衡点稳定性的充分条件.     

A coated rigid elliptical inclusion loaded by a couple in the presence of uniform interfacial and hoop stresses

We consider a confocally coated rigid elliptical inclusion, loaded by a couple and introduced into a remote uniform stress field. We show that uniform interfacial and hoop stresses along the inclusion–coating interface can be achieved when the two remote normal stresses and the remote shear stress each satisfy certain conditions. Our analysis indicates that: (i) the uniform interfacial tangential stress depends only on the area of the inclusion and the moment of the couple; (ii) the rigid-body rotation of the rigid inclusion depends only on the area of the inclusion, the coating thickness, the shear moduli of the composite and the moment of the couple; (iii) for given remote normal stresses and material parameters, the coating thickness and the aspect ratio of the inclusion are required to satisfy a particular relationship; (iv) for prescribed remote shear stress, moment and given material parameters, the coating thickness, the size and aspect ratio of the inclusion are also related. Finally, a harmonic rigid inclusion emerges as a special case if the coating and the matrix have identical elastic properties.     

Some model problems of dynamics for a rigid body interacting with a medium

The paper addresses the stability of solutions of ordinary differential equations of particular type for different statements and assumptions. The equations are interpreted as models of motion of a rigid body under the action of the ambient medium __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 49–67, October 2007.     

基于状态观测器的带分布参数体系地震响应控制

针对带分布参数体系地震响应控制问题,建立带分布参数体系的运动控制方程,推导出应用于带分布参数体系的序列最优模态控制算法。根据序列最优模态控制算法振动控制时对结构全状态反馈的需要,提出了针对序列最优模态控制算法的全维状态观测器,形成基于全维状态观测器的序列最优模态控制算法,然后通过测量容易测量的结构地震响应,由全维状态观...     

一种基于轮轨竖向刚性接触的车-桥空间耦合振动建模方法

车辆-桥梁耦合振动研究具有重要的理论意义和工程实用价值,耦合系统运动方程的建立是研究开展的关键。本文将车辆-桥梁作为一个整体系统,采取轮轨竖向刚性接触方式,考虑轨道竖向、横向不平顺及其一、二阶导数,和轮对侧滚惯性力以及自旋角动量的影响,车辆采用弹簧阻尼连接的多刚体模拟,桥梁采用空间梁单元离散,基于Kalker线性蠕滑理论结合Shen-Hedrick-Elkins修正理论计算轮轨蠕滑力,运用弹性系统动力学总势能不变值原理及其对号入座法则,推导了车辆-桥梁耦合系统空间有限元形式的运动方程,该运动方程可采用逐步积分法直接求解得到车辆和桥梁的动力响应。最后,本文给出了典型的数值算例进行了分析计算。     

Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters

Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.     

Reduced model of a rotor-shaft system using modified SEREP

A modified System Equivalent Reduction Expansion Process (SEREP) is reported to reduce large linear system-equations of motion, which also include gyroscopic effect, internal and external damping. The process is employed on equations of motion written in state-space and utilizes both right and left eigenvectors of the original system unlike only the former in conventional SEREP approach. Numerical example with a finite element model representing multi-disc rotor-shaft-bearing-dynamics shows effectiveness of the process. Nice agreement of Campbell diagrams, FRF plots and unbalance response amplitude between reduced and original systems show usefulness of the reduction process.     

STABILITY OF MOTION FOR A CONSTRAINED BIRKHOFF'S SYSTEM IN TERMS OF INDEPENDENT VARIABLES

I.IntroductionInl927,AmericanmathematicianG.D.Birkh0ffgaveakindofequationsofdynamicswhichweremoregeneralthantheHamilton'sequationsinhiswork"DynamicalSystems-l'].TheequationsarecalledBirkhofCsequationssuggested.byAmericanphysicianR.M.SantiIIiinl978[2j.Inl9…     

Issues of stability and accuracy in identifying the principal axis of inertia of an inhomogeneous rigid body with a rotating Hooke’s joint

The paper addresses issues of real-world operation of a device designed to experimentally identify the principal central axes of inertia of an arbitrary inhomogeneous rigid body. The effect of external and internal dissipation on the stability and accuracy of the device is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 131–143, November 2006.     

Stability analysis of a noise control system in a duct by using delay differential equation

The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed- loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoretical results.     

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier–Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time‐dependent. Since the numerical control problem is ill‐posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60?Re?140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A significant reduction of the amplitude of the variation of the drag coefficient is obtained for the optimized values of the rotation rate. Copyright © 2002 John Wiley & Sons, Ltd.     

Shape optimization of a body located in incompressible flow using adjoint method and partial control algorithm

The purpose of this study is to obtain an optimal shape of a body located in an incompressible viscous flow. The optimal shape of the body is defined so as to minimize the fluid forces acting on it by determining the surface coordinates based on the finite element method and the optimal control theory. The performance function, which is used to judge the optimality of a shape, is defined as the square sum of the drag and lift forces. The minimization problem is solved using an adjoint equation method. The gradient in the adjoint equation is affected by the finite element configuration. The use of a finite element mesh whose shape is appropriate for the procedure is important in shape optimization. If the finite element mesh used is not suitable for computations, the exact gradient is not calculated. Therefore, a structured mesh is used for the adjacent area of the body and all finite element meshes are refined using the Delaunay triangulation at each iteration computation. The weighted gradient method is applied as the minimization technique. Using an algorithm in which all nodal coordinates on the surface of the body are employed and starting from a circle as an initial shape, a front‐edged and rear‐round shape is obtained because of the vortices at the back of the body. To overcome this difficulty, we introduced the partial control algorithm, in which some of the nodal coordinates on the surface of the body are updated. From four cases of computational studies, we reveal that the optimal shape has both sharp front and sharp rear edges. All computations are conducted at Reynolds number Re=250. The minimum value of the performance function is obtained. Copyright © 2010 John Wiley & Sons, Ltd.