Precession Velocity Research Articles

Precession motions of a gyrostat, having a fixed point, in three homogeneous force fields

The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of a gyrostat motion are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations was conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2:1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It was proved that the obtained solutions can be described by elementary functions of time.

On a Method for Integrating the Equations of Rigid Body Motion in Three Homogeneous Force Fields

This paper presents a method for integrating the equations of motion of a rigid body having a fixed point in three homogeneous force fields. It is assumed that under certain conditions these equations admit an invariant relation that is characterized by the following property: the velocity of proper rotation of the body is twice as large as the velocity of precession. The integration of the initial system is reduced to the study of three algebraic equations for the main variables of the problem and one differential first-order equation with separating variables.

Orbital precession in the restricted three-body problem: Exact representations

Analytical representations for the rate of apsidal precession in the planar elliptical restricted three-body problem are considered in the case when the orbit of the disturbing body is external to the orbit of the test particle. Analytical expressions are compared with numerical data obtained during numerous calculations of the precession rate. An analytical expression is obtained for the apsidal precession velocity in the form of a power series with a parameter equal to the ratio of the semi-major axes of the orbits of the test particle and the disturbing planet. It is shown that the analytical expressions for the velocity of the apsidal precession of the particle are reliable only at distances not close to the instability zone near the orbit of the disturbing planet. Near the Wisdom gap, the linear secular theory stops working. A correction empirical formula is proposed for calculating the apsidal precession rate at relatively high (less than 0.5) eccentricities of the particle and the disturbing planet. The proposed formulas are applied to the description of the precession of orbits in real exoplanetary systems.

The motion of a washer on a vertical steel rod

A washer on a vertical steel rod may start spinning instead of simply sliding down. The forces on the washer are analyzed, and the relationship between the angular velocity of rotation and the angular velocity of precession is obtained. A relationship about the coefficient of friction of the washer is obtained at the condition of rotation without slipping. The influence of the coefficient of friction and the ratio of the inner diameter of the washer to the diameter of the rod on the sliding state was investigated experimentally, and a two-dimensional phase diagram of the rotation without slipping was obtained. The relationship between the three parameters(the nutation angle of the washer, the angular velocity of precession, and the final vertical velocity) and the ratio of the inner diameter of the washer to the diameter of the rod in the condition of rotation without slipping was further investigated. The experimental results are in good agreement with the theoretical equations.

Signatures of a spinning supermassive black hole binary on the mas-scale jet of the quasar S5 1928+738 based on 25 yr of VLBI data

ABSTRACT In a previous work, we have identified the spin of the dominant black hole of a binary from its jet properties. Analysing Very Long Baseline Array (VLBA) observations of the quasar S5 1928+738, taken at 15-GHz during 43 epochs between 1995.96 and 2013.06, we showed that the inclination angle variation of the inner (<2 mas) jet symmetry axis naturally decomposes into a periodic and a monotonic contribution. The former emerges due to the Keplerian orbital evolution, while the latter is interpreted as the signature of the spin-orbit precession of the jet emitting black hole. In this paper, we revisit the analysis of the quasar S5 1928+738 by including new 15-GHz VLBA observations extending over 29 additional epochs, between 2013.34 and 2020.89. The extended data set confirms our previous findings which are further supported by the flux density variation of the jet. By applying an enhanced jet precession model that can handle arbitrary spin orientations κ with respect to the orbital angular momentum of a binary supermassive black hole system, we estimate the binary mass ratio as ν = 0.21 ± 0.04 for κ = 0 (i.e. when the spin direction is perpendicular to the orbital plane) and as ν = 0.32 ± 0.07 for κ = π/2 (i.e. when the spin lies in the orbital plane). We estimate more precisely the spin precession velocity, halving its uncertainty from $(-0.05\pm 0.02)$ to $(-0.04\pm 0.01)^{\circ }\, \mathrm{yr}^{-1}$.

Coulomb Problem for Classical Spinning Particles

We consider the motion of a weakly relativistic charged particle with an arbitrary spin in central potential e/r in terms of classical mechanics. We show that the spin–orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The angular velocity of precession depends on the distance of the particle from the centre. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin–orbital interaction. The possible orbits of a quantum particle are determined by the Bohr–Sommerfeld quantization rule. We give examples of orbits corresponding to small quantum numbers, which were obtained by numerical integration of equations of motion. The energies of stationary states are determined by spin–orbital interaction.

On a Class of Precessions of a Rigid Body with a Fixed Point under the Action of Forces of Three Homogeneous Force Fields

This paper is concerned with a special class of precessions of a rigid body having a fixed point in a force field which is a superposition of three homogeneous force fields. It is assumed that the velocity of proper rotation of the body is twice as large as its velocity of precession. The conditions for the existence of the precessions under study are written in the form of a system of algebraic equations for the parameters of the problem. Its solvability is proved for a dynamically symmetric body. It is proved that, if the ellipsoid of inertia of the body is a sphere, then the nutation angle is equal to $\arccos\frac{1}{3}$. The resulting solution of the equations of motion of the body is represented as elliptic Jacobi functions.

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.

Tidal effect on the gyroscopic precession around a compact star

General relativistic effects around massive astrophysical objects can be captured using a test gyro orbiting the object in a circular geodesic. This paper discusses how the tidal field due to a companion object affects the spin precession frequency and orbital angular velocity of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. The central object is either a neutron star or a white dwarf in this study. The test gyro is any planetary or asteroid-like object orbiting a neutron star or a white dwarf. Moreover, the companion object that causes the tidal field can be a neutron star, white dwarf or a stellar black hole. It is seen that the tidal effect significantly affects the spacetime around the central object, which affects the gyro precession frequency and the orbital angular velocity. Slow rotation approximation has been considered for the central object, which creates negligible deformation. The change in the gyro’s precession frequency and the orbital angular velocity due to the tidal field increases with an increase in the companion object’s mass and decreases as the separation between the central star and the companion star increases. The tidal effect also varies with the stiffness of the equation of state of matter describing the host star. The lower the compactness of the host star, the greater is the tidal response; thus the greater is the change in the gyro’s precession and angular velocity of the geodesic.

Early evolution of a newborn magnetar with strong precession motion in GRB 180620A

ABSTRACT The observed early X-ray plateau in the afterglow lightcurves of some gamma-ray bursts (GRBs) is attributed to the dipole radiations (DRs) of a newborn magnetar. A quasi-periodic oscillation (QPO) signal in the plateau would be strong evidence of the magnetar precession motion. By making a time-frequency domain analysis for the X-ray afterglow lightcurve of GRB 180620A, we find a QPO signal of ∼650 s in its early X-ray plateau. We fit the lightcurve with a magnetar precession model by adopting the Markov chain Monte Carlo algorithm. The observed lightcurve and the QPO signal are well represented with our model. The derived magnetic field strength of the magnetar is $B_{\rm p}= (1.02^{+0.59}_{-0.61})\times 10^{15}$ G. It rapidly spins down with angular velocity evolving as Ωs ∝ (1 + t/τsd)−0.96, where τsd = 9430 s. Its precession velocity evolution is even faster than Ωs, i.e. Ωp ∝ (1 + t/τp)−2.18 ± 0.11, where τp = 2239 ± 206 s. The inferred braking index is n = 2.04. We argue that the extra energy loss via the magnetospheric processes results in its rapid spin-down, low braking index, and strong precession motion of the magnetar.

Multipole analysis on gyroscopic precession in f(R) gravity with irreducible Cartesian tensors

In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/{c}^{3}$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of general relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a pointlike or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of gravitoelectric-type precession, gravitomagnetic-type precession, $f(R)$ precession, and Thomas precession are all derived. The first two types of precession are collectively called general relativity-like precession, and the $f(R)$ precession is the correction in $f(R)$ gravity. At the leading pole order, these expansions can recover the results for the gyroscope moving around a pointlike or ball-like source. If the gyroscope has a nonzero four-acceleration, its spin's total angular velocity of precession up to $1/{c}^{3}$ order in $f(R)$ gravity is the same as that in general relativity.

Vortex precession and exchange in a Bose-Einstein condensate

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.

Precessional angular velocity and field strength in the complex octonion space

The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational fields. One formula can be derived from the octonion torque, calculating the precessional angular velocity generated by the gyroscopic torque. When the octonion force is equal to zero, it is able to deduce the force equilibrium equation and precession equilibrium equation and so forth. From the force equilibrium equation, one can infer the angular velocity of revolution for the particles. Meanwhile, from the precession equilibrium equation, it is capable of ascertaining the precessional angular velocity induced by the torque derivative, including the angular velocity of Larmor precession. Especially, some ingredients of torque derivative are in direct proportion to the field strengths. The study reveals that the precessional angular velocity induced by the torque derivative is independent of that generated by the torque. The precessional angular velocity, induced by the torque derivative, is relevant to the torque derivative and the spatial dimension of precessional velocity. It will be of great benefit to understanding further the precessional angular velocity of the spin angular momentum.

Анализ особенностей реализации схемы полета блока выведения при запуске микрокосмических аппаратов на промежуточную орбиту с синхронной прецессией

The article considers features of the implementation of the launching scheme for a group of small spacecraft at the stage of the Volga type launch unit operation during the transition from the reference orbit formed by the “Soyuz 2.1 v” launch vehicle to the intermediate orbit, where the small spacecraft separate. The orbit with synchronous precession velocity of the ascending node longitude with respect to the working orbit is chosen as an intermediate orbit, to which the small spacecraft transfer independently, using their propulsion system, after separation from the launch unit. The article solves the problem of choosing the rational orientation of the launch unit during the release of pulses, in the passive flight segments, as well as for the safe separation of the small spacecraft in an intermediate orbit with synchronous precession. Parameters of maneuvers to flood launch unit after separation of small spacecraft are calculated. Numerical results of fuel consumption for direct deorbiting and selection of maneuvering intervals for launch unit submersion in a given area of the world ocean are obtained. The calculations of the Earth shadow- and semishadow-sunlight time for small spacecraft are performed.

Models for Velocity Decrease in HH34

The conservation of the energy flux in turbulent jets that propagate in the interstellar medium (ISM) allows us to deduce the law of motion when an inverse power law decrease of density is considered. The back-reaction that is caused by the radiative losses for the trajectory is evaluated. The velocity dependence of the jet with time/space is applied to the jet of HH34, for which the astronomical data of velocity versus time/space are available. The introduction of precession and constant velocity for the central star allows us to build a curved trajectory for the superjet connected with HH34. The bow shock that is visible in the superjet is explained in the framework of the theory of the image in the case of an optically thin layer.

Spin angular momentum of proton spin puzzle in complex octonion spaces

The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.

Describing electromagnetic and strong interactions in rotating frames in collisions of high energy nuclei

Interaction between quarks in rotating reference frames described by the vector or scalar Cornell potential is considered. The vector potential is similar to the electromagnetic potential. The precise relativistic Hamiltonian in the Foldy–Wouthuysen representation for terms of the zeroth and first orders in the Planck constant and such terms of the second order that describe contact interactions is rigorously derived. The classical limit of this Hamiltonian, which is also precise for terms of the zeroth and first orders in the Planck constant, is determined for the first time. Electromagnetic interaction is also taken into account. General expressions for the angular velocity of spin precession corresponding to the high energy of the spin–orbit interaction for both the vector and scalar Cornell potential are derived. For the both potentials, we present dependences of the angular velocity of spin precession on the forces acting on a quark, which can in principle be determined by analyzing the kinematics of particle jets emitted upon collisions. The final estimate of spin–orbit interaction (on the order of GeV) demonstrates the great magnitude of the effect.

Can gravitation anisotropy be detected by pendulum experiments?

After some 170 years of Foucault pendulum experiments, the linear theory fails to quantitatively explain the results of any honest meticulous experiment. The pendulum motion usually degenerates into elliptical orbits after a few minutes. Moreover, unexplained discrepancies up to ± 20% in precession velocity are not uncommon. They are mostly regarded as a consequence of the elliptic motion of the bob associated with suspension anisotropy or as a lack of care in starting the pendulum motion. Over some 130 years, an impressive amount of talented physicists, engineers and mathematicians have contributed to a better partial understanding of the pendulum behaviour. In this work, the concept of biresonance is introduced to represent the motion of the spherical pendulum. It is shown that biresonance can be represented graphically by the isomorphism of the Poincare sphere. This new representation of the pendulum motion greatly clarifies its natural response to various anisotropic situations, including Airy precession. Anomalous observations in pendulum experiments by Allais are analyzed. These findings suggest that a pendulum placed within a mass distribution such as the earth, the moon and the sun should be treated as an interior problem, which can better be addressed by Santilli's new theory of gravitation than by those of Newton and Einstein.

Precessive sand ripples in intense steady shear flows

We describe experimental observations of fully developed, large-amplitude bars under the action of a shearing fluid. The experiments were performed in an annular tank filled with water and sheared above by a steady motor source. The same steady shearing flow can produce a variety of different erodible bed manifestations: advective or precessive bars, which refer to bar structures with global regularity and a near-steady precession velocity; interactive bars, the structure of which depends on local rearrangements, which are in turn a response to complex background topography; and dispersive bars, which are created when an initially isolated mound of sand evolves into a train of sand ripples. Of these, the most amenable to analysis are the precessive bars. For precession bars, we find that the skin depth, which is the nondimensionalized mean-field transport rate, grows exponentially as a function of the shear velocity. From this, we arrive at an analytical expression that approximates the precession speed of the bars as a function of shear velocity. We use this to obtain a formula for sediment transport rate. However, in intense flows, the bars can get large engendering boundary layer separation, leading to a different dynamic for bar formation and evolution. Numerical flow calculations over an experimentally obtained set of precessive bars are presented and show that classical parametrizations of mass flux in terms of bottom gradients have shortcomings. Within the range of shear rates considered, a quantity that does not change appreciably in time is the aspect ratio, which is defined as the ratio of the average bar amplitude, with respect to a mean depth, to the average bar length.

‘It Has to Go Down a Little, in Order to Go Around’ — Revisiting Feynman on the Gyroscope

In this paper we show that with the help of accessible, teaching-quality equipment, some interesting and important details of the motion of a gyroscope, which are typically overlooked in introductory courses, can be measured and compared to theory. We begin by deriving a simple relation between the dip angle of a gyroscope released from rest and its precession velocity. We then describe an experiment that measures these parameters. The data are in excellent agreement with the theoretical prediction. The idea for this project was suggested by the discussion of gyroscopic motion in The Feynman Lectures on Physics. Feynman's (Fig. 1) conclusion (stated in colloquial language and quoted in the title) is confirmed and, in addition, conservation of angular momentum, which underlies this effect, is quantitatively demonstrated.