Regular Precession Research Articles

Stability of Regular Precessions of a Body with a fixed point bounded by the Ellipsoid of Revolution in a Flow of Particles

Stability of Regular Precessions of a Body with a fixed point bounded by the Ellipsoid of Revolution in a Flow of Particles

Stability of Regular Precessions of a Body with a Fixed Point Bounded by the Ellipsoid of Revolution in a Flow of Particles

Stability of regular precessions of a rigid body bounded by the ellipsoid of revolution in a free molecular flow of particles is studied. Conditions of stability of regular precessions of the body are obtained and the Poincare–Chetaev bifurcation diagrams are constructed.

Stability of Regular Precessions of a Body with a Fixed Point Bounded by the Ellipsoid of Revolution in a Flow of Particles

Stability of Regular Precessions of a Body with a Fixed Point Bounded by the Ellipsoid of Revolution in a Flow of Particles

Stabilization of Regular Satellite Precessions Using Lorentz Force Moments

Stabilization of Regular Satellite Precessions Using Lorentz Force Moments

Regular Precession of a Gyrostat in Three Force Fields

Regular Precession of a Gyrostat in Three Force Fields

Controlled motion modes of a gyroscopic pendulum in a gimbal suspension

The issues of controlling the motion of a gyroscopic pendulum fixed in a gimbal suspension and having three degrees of freedom are discussed in the paper. It is proposed to use physical analogies and correlate their action with the dissipative forces of external viscous friction, friction in gimbal joints and internal friction in the pendulum rod, as well as inertial forces and gyroscopic forces to form the control torques in gimbal joints. Six modes of controlled movement of the system are considered, which allow achieving various goals. It is shown that it is possible to completely suppress the motions of a gyroscopic pendulum, switch it to the mode of a spherical or physical pendulum, enter the mode of rotation around a fixed vertical axis, bring it to the mode of regular precession, and also strengthen or weaken the gyroscopic structure of the motion equations. The discussion of these modes of controlled motion is accompanied by the construction of motion equations both within the framework of the original nonlinear model and for simplified linear or weakly nonlinear models. The obtained results are theoretically interesting and may be useful for specific practical applications in the field of gyroscopic technology.

Perfect nonradiating electromagnetic source and its self-action

Nonradiating sources and anapoles are curious objects from the physics of invisibility that illuminate subtle concepts of fundamental electrodynamics and have promising applications in nanophotonics. The present work shows that a perfectly conducting sphere with a hidden magnetic field is a simple nonradiating electromagnetic source with mechanical excitation and complete internal confinement of electromagnetic energy. It does not require external electromagnetic excitation and is excited by rotation, which induces internal charges and currents with a self-compensating external radiation. The constructed source acts on itself through Lorentz forces emerging from the interaction of charges and currents with electromagnetic fields inside the sphere and, when having a freedom of rotation about the fixed center, exhibits regular precession like a gyroscope. This self-action reveals an internal electromagnetic activity of the perfect nonradiating source, externally inactive and invisible. Neutron stars, these nanospheres of space, can be such natural nonradiating sources when their magnetic fields are buried.

Regular Precession of a Gyrostat in Three Force Fields

The article gives a solution to the problem of possible conditions of regular precession in the motion of a gyrostat around a fixed point under the action of two uniform and one inhomogeneous field. For the known case with equal precession and proper rotation velocities, new solutions are indicated with the precession axis deviated from the symmetry axis of the inhomogeneous field. New cases of regular precession are found, when the ratio of precession and proper rotation velocities is equal to two or one second. Application of the results to precession in orthogonal fields and to precession of a solid are considered.

On Libration Points in the Asteroid–Research Probe System

This paper is dedicated to a study of relative motion in the field of homogeneous spheroid bodies. It is assumed that an asteroid’s satellite does not affect its translational and rotational motion by inertia. The latter motion has the form of rotation in the mode of regular precession. The case in which the asteroid is an ellipsoid of revolution is considered. A system of conditions that the libration points must satisfy is constructed; it is shown that its solution is two types of libration points, which differ in their location with respect to the constant vector of the angular momentum and the axis of symmetry of the ellipsoid. Thereafter, the stability of libration points is investigated numerically and analytically in the first approximation.

Sufficiently small rotations of Lagrange’s gyro

In this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmetry one and a restoring torque that is considered to be greater than the perturbing one. In this manner, we replace the familiar small parameter that was used in previous works with a large one. In such cases, the gyro equations for motion (EOM) are formulated in the form of a two-degrees-of-freedom (DOF) autonomous system. We average the obtained system to get periodic solutions and motion’s geometric interpretation of the problem using the large parameter. The regular precession and the pure rotation of the motion are obtained. A numerical study is evaluated for asserted the used techniques and showed the influence of the changing parameters of motion on the gyro behavior. The trajectories of the motions and their stabilities are discussed and analyzed. The novelty of this work lies in how to adapt the method of large parameter (MLP) to solve the rigid body problem, especially since it has been assumed initially that its angular velocity or its initial energy are very small. MSC (2000): 70E20, 70E17, 70E15, 70E05

Postflight Recovery of the Rotational Motion of a Small Space Vehicle from Solar Sensor Information

The use of the developed technology for solving inverse problems of parametric identification of the rotational motion of a spacecraft (SC) based on the accumulated sample of measurements of various compositions is expanded. On the example of processing telemetry data (measuring the direction vector to the Sun) of the BugSat-1 small spacecraft (SSC), the possibility of determining not only the characteristics of rotational motion but also its inertia coefficient is demonstrated. The rotational motion is determined based on the data obtained for five time intervals from January to May 2022, during which BugSat-1 made an uncontrolled movement around the direction vector toward the Sun. This type of motion does not allow applying traditional approaches to determine the dynamics of its rotation. In the process of data processing, a simplified model of the rotation of a SSC is used. At the same time, the initial conditions of rotational motion are estimated—the angular velocity vector and orientation angles, which made it possible to draw a conclusion about the precessional motion of a SSC. Using the analytical model of a regular precession, it is possible to estimate the inertia coefficient of a SSC. The results of flight information processing are presented and the errors of the obtained results are estimated.

Precession Dynamics of the Uniaxial Nanoparticle Magnetization in the Ferromagnetic Resonance Region

The influence of the shape parameter (oblateness) of a uniaxial ellipsoidal nanoparticle on the dynamics of its magnetic moment upon magnetization along the symmetry axis and excitation by a weak transverse high-frequency field in the region of parameters where the equilibrium magnetic moment of the nanoparticle and the external static field is noncollinear has been studied. It is shown that as the oblateness increases, the irregularity of the oscillations increases, which at first affects only their amplitude, but then also the time dependence. The intervals of the shape parameter (or frequency), where various nonlinear modes of precession are realized --- dynamic bistability, complex spatial attractors and chaos, were revealed using bifurcation diagrams. Keywords: ellipsoidal nanoparticle, "easy" axis, effective anisotropy, ferromagnetic resonance, high frequency field, bistability, regular and chaotic precession.

Regular precession of a rigid body in two uniform fields

This article describes all possible cases of regular precession in the motion of a rigid body around a fixed point under the action of two uniform fields. A generalization of the known Yehia conditions is obtained when the precession and proper rotation velocities are equal to each other. A new case of regular precession is found for which the precession velocity is twice the proper rotation velocity, the precession axis may not be orthogonal to the force lines of both fields and is not orthogonal to the proper rotation axis.

Regular Precession of a Gyrostat in Three Uniform Fields

Regular Precession of a Gyrostat in Three Uniform Fields

Dynamics of magnetization of a uniaxial nanoparticle in the region of noncollinear ferromagnetic resonance

Resonance dynamics of the magnetic moment of a uniaxial ellipsoidal nanoparticle under its magnetic biasing along the symmetry axis and excitation by a transverse high-frequency field is studied with the parameters (frequency, magnetic bias field and shape parameter), corresponding to the noncollinear orientation of equilibrium magnetization and the external static field. We revealed the frequency regions where precession becomes nonlinear at a weak alternating field and dynamic bistability, as well as complex spatial attractors and chaos are implemented. Keywords: ellipsoidal nanoparticle, ferromagnetic resonance, static and high-frequency field, nonlinearity, effective anisotropy, bistability, regular and chaotic precession.

On the Stabilization of the Regular Precessions of Satellites by Means of Magnetic Moments

On the Stabilization of the Regular Precessions of Satellites by Means of Magnetic Moments

Effect of the Gravity and Magnetic Field to Find Regular Precessions of a Satellite-gyrostat with Principal Axes on a Circular Orbit

We consider the motion of a magnetized satellite-gyrostat in a circular orbit due to the combined influence of uniform gravity and magnetic fields. Based on the Lagrangian equations, the necessary conditions for the existence of regular precessions are determined in which the axis of precession is perpendicular to the orbital plane. All possible regular precessions and permanent rotations are determined and classified. We show the usage of Lagrange equations taking Eulerian angles as generalized coordinates for determining the regular precessions is more effective and accurate than utilization of Euler-Poisson equations.

Numerical approach for bifurcation and orbital stability analysis of periodic motions of a 2-DOF autonomous Hamiltonian system

In Spaceflight Dynamics it is often necessary to obtain periodic motions of conservative mechanical systems and analyze their stability and bifurcation. These conservative systems can be described using Hamiltonian equations. We consider bifurcation and orbital stability problem for periodic motions of a 2-DOF autonomous Hamiltonian system. Since it is not possible to obtain analytical solutions to the aforementioned problem for all admissible values of its parameters a two-step numerical approach is proposed. On the first step the so-called base solutions are obtained analytically for particular values of problem’s parameters. The base solutions are then continued to the borders of their existence domains using a numerical algorithm. In course of computation bifurcation points are identified and orbital stability is studied. On the second step new base solutions are identified in the neighborhood of bifurcation points and the continuation process is repeated. Finally, orbital stability and bifurcation diagrams of the resulting families of periodic motions are constructed. Poincare sections are also computed in the neighborhoods of bifurcation points to verify the results. To illustrate this approach, we computed the bifurcation and orbital stability diagrams for families of short-periodic motions originating from Regular precessions of a dynamically-symmetric satellite.

Experimental estimation of efficiency and kinematic accuracy of a spherical roller transmission

Spherical roller transmissions with double-row pinions provide high reduction ratios in drives with a compact and lightweight design. The transmissions can be used as mechanical modules in kinematic chains of robots and manipulators. The pinion has two rows of coaxially arranged rollers and, when in operation, performs a regular precession. The paper examines the characteristics of an experimental model of a speed reducer with a spherical roller transmission with a reduction ratio of 44. The arrangement of the test rig as well as the test instruments and methods are described. The results of experimental study determining the efficiency of a spherical roller transmission depending on the torque being transmitted and the rotational speed of the drive shaft are presented. It has been found that the mean efficiency of the speed reducer is within the range of 0.7 … 0.8 and its maximum value is 0.81, which corresponds to the efficiency of worm gears with similar characteristics. The theoretical calculations for determining the efficiency, which were obtained in previous studies, have been confirmed; the value of the reduced friction coefficient has been calculated. The constancy of the efficiency and the reduction ratio of the experimental model of the speed reducer and the factors influencing this constancy have been investigated.

Analysis of contact strength of spherical roller transmission with double-row pinion

This paper presents a detailed description of the design of the spherical roller transmission. The pinion has two rows of rollers; the axes of the rollers are located on conical surfaces. When the transmission is operating, the pinion performs a regular precession and the rollers are in contact with the teeth of the stationary and driven central gears. The transmission provides high reduction ratios in a lightweight, compact package. The center of mass of the pinion is located on the axis of rotation of the drive shaft, which reduces the axial moment of inertia and improves the balance of the system compared to double-pinion planetary gears mounted on the drive shaft with eccentricity. Rolling bodies are used in place of teeth, which leads to improved efficiency. The main performance criterion is the contact strength of the teeth of the driven central gear. An equation to calculate maximum contact stresses has been derived by using Hertz theory. An algorithm for calculating the number of the rollers simultaneously engaged and transferring the load is proposed.