自由陀螺体永久转动的稳定性及分叉

自由陀螺体是双自旋卫星或带控制飞轮卫星的动力学模型。本文分析自由陀螺体永久转动的全局特性。利用动量矩积分建立降价的动力学方程,並根据奇点理论对陀螺体永久转动轴的个数和位置以及永久转动的稳定性和分叉现象给出定性解释。     

静电陀螺监控器的导航方程和自对准

本文介绍了几何式静电陀螺监控器的基本结构、工作原理和导航方程；并着重介绍了静电陀螺监控器的自对准。由于几何式静电陀螺监控器的工作特点，在对准时，只需精确的位置座标而不需要航向信息。根据极轴陀螺的动量矩轴绕地球极轴的圆运动，用卡尔曼滤波技术对陀螺框架上的角度传感器输出进行数据处理，即可估计航向角和极轴陀螺的动量矩轴相对地球地轴的初始偏差角。     

静电陀螺监测器中静电陀螺仪的漂移误差模型

本推导了静电陀螺仪转子动量矩的运动方程,根据此方程并应用向量场理论,将造成静电陀螺漂移的外部干扰力矩划分为守恒力矩和非守恒力矩两部分。按照进动规律,最终得到静电陀螺监控器中陀螺仪漂移误差模型的全量形式。     

关于刚体平面运动中动量矩定理的综合讨论

本文从对图形平面上任意动点的动量矩定理这个最一般形式出发,把刚体平面运动中存在的各种形式的动量矩定理都统一起来,同时澄清有关动量矩和动量矩定理中某些流行的模糊概念.1.符号规定和说明(图1)定坐标系 O-ξη,质心平动坐标系 c-ξ′η′,质心随动坐标系 c-xy(连同平面图形-体运动),任意...     

静电陀螺仪光电信号器

空心转子静电陀螺仪通常采用光电信号器进行动量矩位置信息的读取。光电传感器的分辨率、零位噪声和光轴稳定性对陀螺漂移精度和长期工作稳定性有直接影响。本文对静电陀螺仪光电信号器工程实践中的有关理论和技术问题作了较为详细的论述。     

H调制陀螺监控高精度惯性导航系统

对于由单自由度液浮陀螺仪构成的平台式惯性导航系统,H调制陀螺监控技术可以同时对三个导航陀螺分别进行监控和漂移自补偿,它采用北向和方位H调制陀螺监控方案,在惯性平台台体上加装北向和方位监控陀螺,对北向和方位导航陀螺进行监控,实现误差自补偿。监控陀螺采取力反馈工作方式,其输入轴与相应导航陀螺的输入轴同向平行。通过改变监控陀螺电机的转速,使其周期性工作在不同的动量矩H值上,并保证不同H值之间监控陀螺调制漂移的稳定性。根据不同H值下的监控陀螺输出,即可解算出相应导航陀螺的漂移并随时加以补偿。经过室内试验、码头系泊试验和海上航行试验的考核,结果表明,H调制陀螺监控高精度惯性导航系统其定位误差最大值≤1.50 nmile/72 h,CEP≤0.90 nmile/72 h,系统重调周期可以延长至3～5昼夜。     

关于陀螺近似理论的讨论

本文直接从质点系动量矩定理出发,导出了刚体规则进动动力学方程.在此基础上,讨论了陀螺近似理论公式的适用条件,将原有条件中的质量分布特性由旋转体扩展到一定条件下的非旋转体,将运动特性由高速自转扩展为一定条件下的非高速自转.     

猫下落时的翻身与运动生物力学

<正> 用双手托起一只猫,使它四脚朝天,然后突然撒手;猫在下落过程中,竟能在空中翻身,四脚朝地安全落下.这种现象早已为大家熟悉,但在力学原理上却不容易解释.因为猫在下落的初始时刻对质心的动量矩为零,而下落过程中猫所受的重力对质心的力矩也为零;根据动力学中相对质心的动量矩定理,猫对其质心的动量矩,特别是对猫体纵轴(头尾连线)的动量矩,应该守恒,即永远为零.所以当猫的前半身转体时,后半身要向相反方向转体,而不可能整个身子向一个方向转     

猫下落时的翻身与运动生物力学

用双手托起一只猫,使它四脚朝天,然后突然撒手;猫在下落过程中,竟能在空中翻身,四脚朝地安全落下.这种现象早已为大家熟悉,但在力学原理上却不容易解释.因为猫在下落的初始时刻对质心的动量矩为零,而下落过程中猫所受的重力对质心的力矩也为零;根据动力学中相对质心的动量矩定理,猫对其质心的动量矩,特别是对猫体纵轴(头尾连线)的动量矩,应该守恒,即永远为零.所以当猫的前半身转体时,后半身要向相反方向转体,而不可能整个身子向一个方向转     

舰载旋转机械基础冲击响应建模和数值计算

针对舰载旋转机械的水下非接触爆炸冲击动力学响应问题,提出了一种基础冲击转子-轴承系统建模理论.结合牛顿运动定理、动量矩定理和Timoshenko梁理论,推导出了系统动力学微分方程,方程综合考虑了转子的旋转惯性力、剪切力、陀螺效应、轴向力、轴向扭矩以及轴承的油膜力.通过在时间域和空间域分别采用直接积分法和Galerkin...     

万有引力场中陀螺体的混沌运动

研究万有引力场中沿圆轨道运行的非对称陀螺体的姿态运动,引入Ｄｅｐｒｉｔ正则变量建立系统的Ｈａｍｉｌｔｏｎ结构,利用Ｍｅｌｎｉｋｏｖ方法证明在万有引力短作用的昆体产生混沌运动的可能性。对Ｐｏｉｎｃａｒｅ截面的数值计算表明提高陀螺体的转子转速可对混沌起抑制作用。     

On a class of motions of a Zhukovskii gyrostat with variable gyrostatic moment

The paper deals with the problem of Zhukovskii gyrostat motions in the case of a constant angle between the gyrostat invariable axis and the gyrostat angular momentum vector. It is assumed that the gyrostatic moment depends on time. The obtained conditions on the gyrostat parameters and the expression for the gyrostatic moment characterize a new solution of the Zhukovskii equations with variable gyrostatic moment. We prove that it describes semiregular precession of the first type with respect to the angular momentum vector.     

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations.     

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.     

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。     

Global motion of a dissipative asymmetric gyrostat

Summary The motion of an asymmetrical gyrostat with external or internal energy dissipation is discussed by use of the qualitative method. The attitude motion of the gyrostat is described by two angular coordinates of the total angular momentum H relative to a body-fixed reference frame. The dynamical equation is written for an autonomous system whose singularity corresponds to the permanent rotation of the gyrostat. The global motion of the gyrostat is determined by the number and distribution of singularities. The type of each singularity varies with the variation of mass geometry and rotor speed, and a bifurcation phenomenon can be observed.

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Das globale Verhalten eines dissipativen unsymmetrischen Kreisels

Übersicht Das Verhalten eines asymmetrischen Kreisels mit innerer oder äußerer Reibung wird qualitativ untersucht. Die Stellung des Kreisels wird durch zwei Kardanwinkel zwischen körperfesten und raumfesten Koordinatensystemen beschrieben. Die sich ergebenden Bewegungsgleichungen gelten für autonome Systeme, deren Singularitäten permanente Drehungen des Kreisels darstellen. Das Globalverhalten des Kreisels ist durch die Anzahl dieser Singularitäten und ihrer Verteilung gegeben. Die Art einer jeden Singularität ändert sich mit der Masseverteilung und der Rotorgeschwindigkeit, und es treten Verzweigungen auf.

     

Integrable cases in the dynamics of axial gyrostats and adiabatic invariants

This paper presents the study of axial gyrostats dynamics. The gyrostat is composed of two rigid bodies: an asymmetric platform and an axisymmetric rotor aligned with the platform principal axis. The paper discusses three types of gyrostats: oblate, prolate, and intermediate. Rotation of the rotor relative to the platform provides a source of small internal angular momentum and does not affect the moment of inertia tensor of the gyrostat. The dynamics of gyrostats without external torque is considered. The dynamics is described by using ordinary differential equations with Andoyer–Deprit canonical variables. For undisturbed motion, when the internal moment is equal to zero, the stationary solutions are found, and their stability is studied. General analytical solutions in terms of elliptic functions are also obtained. These results can be interpreted as the development of the classical Euler case for a solid, when to one degree of freedom—the relative rotation of bodies—is added. For disturbed motion of the gyrostats, when there is a system with slowly varying parameters, the adiabatic invariants are obtained in terms of complete elliptic integrals, which are approximately equal to the first integrals of the disturbed system. The adiabatic invariants remain approximately constant along a trajectory for long time intervals during which the parameter changes considerably. The results of the study can be useful for the analysis of dynamics of dual-spin spacecraft and for studying a chaotic behavior of the spacecraft.     

On the rotational motion of a gyrostat about a fixed point with mass distribution

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.     

非轴对称陀螺体自激运动的定性分析

研究非轴对称陀螺体在自激控制力矩作用下的姿态运动．将无力矩状态的两个初积分的积分常数T和G^2作为描述自激运动的状态变量建立其微分方程．利用受扰运动在(T，G^2)空间中的相轨迹判断稳态运动的稳定性，并进行了数值验证．     

Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes

To study the stability of steady rotations of a control moment gyro system with internal dissipation, we use the Barbashin-Krasovskii theorem and the relation, established in [1], between the Lyapunov function and steady motions. Taking into account the special properties of the original problem, we reduce it to a lower-dimensional problem.We give a detailed presentation of an algorithm for analyzing the stability of steady motions of a gyrostat and use this algorithm to perform a complete study for two systems consisting, respectively, of one and two gyros whose gimbal axes are parallel to the principal axis of inertia of the system. Each steady motion is identified as either asymptotically stable or unstable. We find periodic motions that exist only in the presence of dynamic symmetry and which are regular precessions. For the system with two gyros, we prove the asymptotic stability of quiescent states and prove that in the angular momentum range where these states are defined the system does not have any other stable motions.