无力矩非对称双自旋卫星的姿态运动

本文从动量矩守恒定律出发,导出以欧拉角及相对转动角为参变量的非对称双自旋卫星在无力矩状态下的一阶运动微分方程组,并利用能量积分获得零马达力矩条件下的解析形式姿态运动规律。以此讨论了转子自转角速度接近零时一类卫星的姿态运动稳定性,及其在消旋过程中通过不稳定区域时的非驻定姿态运动。文中顺便指出并纠正了文献[7]、[10]的错误之处。     

具不对称粘弹性支承弹性盘轴转子系统的非线性动力稳定性分析

考虑轴和盘的质量及轴的几何非线性，建立了在周期轴向载荷作用下具不对称粘弹性支承弹性盘轴转子系统的非线性动力学方程．基于Lyapunov运动稳定性理论和Floquet判据，对系统的线性和非线性动力稳定性进行了分析．     

弹性支承滑动轴承不平衡转子系统非线性动力稳定性和分岔的研究

研究弹性支承滑动轴承不平衡转子系统的稳定性及分岔特性。建立了弹性支承-滑动轴承-转子非线性动力系统的力学模型，在油膜力非线性的情况下，应用数值模拟，采用打靶法计算了刚性转子系统的周期解，并与龙格-库塔法计算的结果进行了对比，依据Floquet理论，分析了周期解的稳定性，再结合龙格-库塔法、Poineare映射法作出了系统运动分岔图。最后，讨论了轴的柔性对转子系统运动稳定性的影响。     

带偏心转子陀螺体的混沌运动

本文讨论了无力矩条件下带有质量偏心轴对称转子的非对称陀螺体的运动。利用动量变量列写动力学方程,并将系统化作受周期微扰作用下的Ｅｕｌｅｒ－Ｐｏｉｎｓｏｔ运动。应用Ｍｅｌｎｉｋｏｖ方法预测系统存在Ｓｍａｌｄ马蹄意义下的混沌运动,此结论与Ｐｏｉｎｃａｒｅ截面的数值计算相符。从Ｐｏｉｎｃａｒｅ截面的相图也可明显看出转子对于双自旋卫星的姿态稳定作用。     

弹性支承滑动轴承－转子系统稳定性的研究

本文研究弹性支承滑动轴承－转子系统的动力稳定性问题，建立了弹性支承滑动轴承－Ｊｅｆｆｃｏｔｔ转子系统的力学模型，采用牛顿延拓法从理论上对该转子轴承系统的动力稳定性进行了分析，讨论弹性支承的刚度对系统稳定性的影响，从而提出提高系统稳定性的有关措施。最后，依据理论分析，利用Ｊｅｆｆｃｏｔｔ转于实验台，作者设计和加工了一副弹性支承器，通过刚性支承和弹性支承两个对比实验，对理论分析的结果进行了验证。实验结果表明，弹性支承能提高转子动力稳定性。     

Jeffcott转子油膜稳定的定性分析

基于Ｍｕｓｓｙｎｓｋａ刚性转子模型,对转子涡动的稳定性进行了分析研究,采用首次近似方程判断了转子涡动方程零解与极限坏的稳定性,确定了转子运动的稳定性条件,在极坐标系下首次给出了用三个状态方程表示的转子轴际系统的简捷方程。     

自旋导弹捷联式陀螺/地磁姿态测量方法

为了解决自旋导弹姿态测量遇到的高自旋角速率超过陀螺量程的问题,提出了一种利用敏感轴垂直于弹轴的双轴微陀螺与三轴地磁传感器组合测量解算自旋导弹姿态的方法.首先,建立了利用三轴地磁场传感器与双轴微陀螺进行姿态测量的解算模型,该模型利用双轴陀螺测得的载体弹轴垂直面的角速度提供俯仰角的微分,结合三轴地磁场传感器的输出解算出当前载体的姿态;接着讨论了模型解算中出现的增根的问题与正确解的判断方法;最后在传感器输出附加白噪声与弹体摆动条件下对该方法进行了仿真,得出在100 s的时间内,1800(o)/s的自旋角速度条件下姿态解算误差角为2°.仿真结果表明该方法可以直接解算三个姿态角均为动态变化的自旋弹的姿态角,因此可用于自旋导弹的姿态测量.     

弹性支承滑动轴承—转子系统稳定性的研究

本文研究弹性支承滑动轴承－转子系统的动力稳定性问题，建立了弹性支承滑动轴承－Ｊｅｆｆｃｏｔｔ转子系统的力学模型，采用牛顿延拓法从理论上对该转子轴承系统的动力稳定性进行了分析，讨论弹性支承的刚度对系统稳定的影响，从而提出提高系统稳定性的有关措施。最后，依据理论分析，利用Ｊｅｆｆｃｏｔｔ转子实验台，作者设计和加工了一副弹性支承器，通过刚性支承和弹性支承两个对比实验，对理论分析的结果进行了验证。实验结果     

微小卫星联合执行机构的递阶饱和姿态控制方法

随着航天飞行任务复杂程度的提高,微小卫星姿态控制系统对实现大角度姿态机动的快速性及稳定性有着较高的要求。考虑到在实际大角度姿态机动过程中力矩饱和及角速度限制的因素,提出了基于欧拉轴转动的递阶饱和模糊PD姿态控制律,同时采用喷气推力器和反作用飞轮作为联合执行机构为微小卫星姿态机动提供大且精确的控制力矩。与传统PD控制律相比,模糊PD姿态控制系统的未知参数可在线自动整定。数学仿真结果表明,基于欧拉轴转动的递阶饱和模糊PD姿态控制系统能够在125 s内实现50.2°的大角度机动,稳定误差能够控制在0.002°之内。与传统PD控制律相比,此方法具有更高的精度及稳定性。     

陀螺相关非孤立系统的不稳定性定理

本文通过定理的证明,提供了一种用来分析有势力及陀螺力作用下可能非孤立系统的不稳定性问题的方法.分析的结论对非线性系统也是正确的.举了两个例子作为定理的应用,并着重分析了二重自旋卫星(或陀螺体卫星)两种姿态的运动稳定性问题.最后就卫星姿态控制中的几个主要研究方向提出了一些看法.     

Balancing a Rotor with Two Coupled Perfectly Rigid Bodies

The steady motions of a vertical rotor balanced by two coupled perfectly rigid bodies (PRBs) are analyzed for stability. The rotor executes plane-parallel motions. The PRBs can rotate together about the rotor axis and about its transverse axes through equal angles but in opposite directions. It is established that when the mass of the PRBs is much less than that of the rotor and the rotor spins with a superresonant speed, only the basic steady motions, which are those of the best-balanced rotor, are asymptotically stable.     

Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part II: Experimental Analysis

In Part I, theoretical analysis of the dynamic behaviour of a rigid rotor with nonlinear elastic restoring forces was carried out. In this part (Part II), an experimental confirmation of the theoretical data from that analysis was sought. With this aim, an experimental model was set up consisting mainly of a practically rigid rotor clamped onto a small diameter piano wire symmetrical to the wire supports. These supports were rigid and equipped with roller bearings and a device that made it possible to adjust the initial tension in the wire so as to make the elastic restoring forces less or more linear. The rotor was dynamically unbalanced and was driven by an asynchronous motor regulated by means of an inverter in order to adjust the rotor speed. A series of tests was performed on this rig with different values of the initial tension in the wire, and the trajectories of two points on the rotor axis were recorded in the course of the tests. These trajectories were obtained, under the hypothesis of similarity, from the orbits covered by two given sections of the wire and detected with two pairs of capacitive transducers. The collected data was compared with the theoretical results from Part I of the present investigation. Comparison of the collected data with the corresponding theoretical results made it possible to infer that system nonlinearity in the presence of small damping can give rise to motions that are periodic, whether synchronous or not, or quasi-periodic, but never chaotic.     

Analytical solutions for dynamics of dual-spin spacecraft and gyrostat-satellites under magnetic attitude control in omega-regimes

The attitude dynamics of a dual-spin spacecraft (a gyrostat with one rotor) with magnetic actuators attitude control is considered in the constant external magnetic field at the presence of the spacecraft’s own magnetic dipole moment, which is created proportionally to the angular velocity components (this motion regime can be called as “the omega-regime” or “the omega-maneuver”). The research of the dual-spin spacecraft angular motion under the action of the magnetic restoring torque is fulfilled in the generalized formulation close to the classical mechanics’ task of the heavy body/gyrostat motion in the Lagrange top. Analytical exact solutions of differential equations of the motion are obtained for all parameters in terms of elliptic integrals and the Jacobi functions. New obtained analytical solutions can be classified as results developing the classical fundamental problem of the rigid body and gyrostat motion around the fixed point. The technical application of the omega-regime to the angular reorientation of the spacecraft longitudinal axis along the angular momentum vector is considered.     

Application of Krein’s theorem and bifurcation theory for stability analysis of a bladed rotor

This paper considers the stability and eigenvalue analyses for a bladed rotor which goes under cylindrical and conical whirling. The model consists of a group of flexible blades which are modeled by beams and rigid disk on the elastic bearings. The model is a Hamiltonian system which is perturbed by small dissipative forces. Krein’s theorem reveals that the forward whirling mode and the blade collective motion may cause instability when their frequencies cut themselves in the Campbell diagram. An unstable interaction between the blades and the conical whirling is discovered. The eigenmode and eigenvalue evolutions are determined on the stability boundary. The bifurcation analysis is performed by applying multiple scales method around the stability boundary. It is shown that the damping distribution between the blades and the bearings may shift the unstable mode.     

基于修正型罗德里格斯参数的三维刚体摆姿态控制

3D 刚体摆是研究地球静止轨道航天器的一个力学简化模型, 它绕一个固定、无摩擦的支点旋转, 具有3 个转动自由度. 文章给出基于修正型罗德里格斯(Rodrigues) 参数描述的3D 刚体摆的姿态动力学方程, 针对3D 刚体摆姿态和角速度稳定的非线性控制设计问题, 基于无源性控制理论利用能量法设计了3D 刚体摆的系统控制器, 并证明了系统满足无源性. 构造了系统的李雅普诺夫(Lyapunov) 函数, 利用能量法设计出3D 刚体摆的姿态控制律, 并由拉萨尔(LaSalle) 不变集原理证明了该控制律的渐近稳定性. 仿真实验给出了3D 刚体摆在倒立平衡位置的姿态和角速度的渐近稳定性, 仿真实验结果表明基于能量方法的3D 刚体摆姿态控制是有效的.     

中心舱体与薄壁梁刚-柔耦合系统的热弹性-结构动力学分析

空间柔性结构受太阳热流冲击而诱发的振动是导致航天器失效的典型模式之一,准确预测结构热致振动的响应及稳定性是卫星设计的基础.针对常见的中心舱体与附属薄壁杆件组成的空间结构,提出了考虑刚-柔耦合、耦合热弹性和耦合热-结构三重耦合效应的热致振动分析理论模型.其中,刚-柔耦合是指舱体姿态角、顶端集中质量转动与柔性附件运动的耦合...     

GENERALIZATION OF KIRCHHOFF KINETIC ANALOGY TO THIN ELASTIC SHELLS 1)

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.     

Kirchhoff动力学比拟对弹性薄壳的推广

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应,在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法.在直法线假设下,在弹性中面上构筑空间正交轴系,此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度.沿两个...     

非线性轴承转子系统稳定性准则的研究

目前对于非线性轴承转子系统，仍普遍采用其线性化系统的对数衰减率作为系统的稳定性判据，这造成了理论和实验结果相差较大。本文对［１］中提出的ＰＣＭ法作了改进，通过对无限长滑动轴承支承对称刚性单盘转子系统的非线性稳定性规律进行的分析，揭示了上述现象的非线性本质，为建立更适用于非线性轴承转子系统的稳定性准则提供参考。