Spinning Body Research Articles

Classical characters of spinor fields in torsion gravity

Abstract We consider the problem of having relativistic quantum mechanics re-formulated with hydrodynamic variables, and specifically the problem of deriving the Mathisson-Papapetrou-Dixon equations (describing the motion of a massive spinning body moving in a gravitational field) from the Dirac equation. The problem will be answered on a general manifold with torsion and gravity. We will demonstrate that when plane waves are considered the MPD equations describe the general relativistic wave-particle duality with torsion, but we will also see that in such a form the MPD equations become trivial.

Dynamics on a submanifold: intermediate formalism versus Hamiltonian reduction of Dirac bracket, and integrability

We consider the Lagrangian dynamical system forced to move on a submanifold Gα(qA)=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_\\alpha (q^A)=0$$\\end{document}. If for some reason we are interested in knowing the dynamics of all original variables qA(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q^A(t)$$\\end{document}, the most economical would be a Hamiltonian formulation on the intermediate phase-space submanifold spanned by reducible variables qA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q^A$$\\end{document} and an irreducible set of momenta pi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_i$$\\end{document}, [i]=[A]-[α]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[i]=[A]-[\\alpha ]$$\\end{document}. We describe and compare two different possibilities for establishing the Poisson structure and Hamiltonian dynamics on an intermediate submanifold: Hamiltonian reduction of the Dirac bracket and intermediate formalism. As an example of the application of intermediate formalism, we deduce on this basis the Euler–Poisson equations of a spinning body, establish the underlying Poisson structure, and write their general solution in terms of the exponential of the Hamiltonian vector field.

Arbitrary controlled re-orientation of a spinning body by evolving its tensor of inertia

Bodies with the nonspherical tensor of inertia (TOI) exhibit a variety of rotational motion patterns, including chaotic motion, stable periodic (quasi-periodic) rotation, unstable rotation around the direction close to the body's second principal axis, featuring a well-known tennis-racket (also known as Garriott-Dzhanibekov [1]) effect – series of seemingly spontaneous 180 degrees flips. These patterns are even more complex if the body's TOI is changing with time. Changing a body's TOI has been discussed recently as a tool to perform controllable Garriott-Dzhanibekov flips and similar maneuvers. In this work, the optimal control of the TOI of the body (spacecraft, or any other device that admits free rotation in three dimensions) is used as a means to perform desirable re-orientations of a body with respect to its angular velocity. Using the spherical TOI as the initial and final point of the maneuver, we optimize the parameters of the maneuver to achieve and stabilize the desired orientation of the body's principal axes with respect to spin angular velocity. It appears that such a procedure allows for finding arbitrarily complex maneuver trajectories of a spinning body. In particular, intermediate axis instability can be used to break the alignment of the body's principal axis and the axis of rotation. Such maneuvers do not require utilization of propellants and could be straightforwardly used for attitude control of a spin-stabilized spacecraft. The capabilities of such a method of angular maneuvering are demonstrated in numerical simulations.

Revisiting the gravitomagnetic clock effect

To the first post-Newtonian order, if two test particles revolve in opposite directions about a massive, spinning body along two circular and equatorial orbits with the same radius, they take different times to return to the reference direction relative to which their motion is measured: it is the so-called gravitomagnetic clock effect. The satellite moving in the same sense of the rotation of the primary is slower, and experiences a retardation with respect to the case when the latter does not spin, while the one circling in the opposite sense of the rotation of the source is faster, and its orbital period is shorter than it would be in the static case. The resulting time difference due to the stationary gravitomagnetic field of the central spinning body is proportional to the angular momentum per unit mass of the latter through a numerical factor which so far has been found to be 4π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\pi $$\\end{document}. A numerical integration of the equations of motion of a fictitious test particle moving along a circular path lying in the equatorial plane of a hypothetical rotating object by including the gravitomagnetic acceleration to the first post-Newtonian order shows that, actually, the gravitomagnetic corrections to the orbital periods are larger by a factor of 4 in both the prograde and retrograde cases. Such an outcome, which makes the proportionality coefficient of the gravitomagnetic difference in the orbital periods of the two counter-revolving orbiters equal to 16π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$16\\pi $$\\end{document}, confirms an analytical calculation recently published in the literature by the present author. It is an important result in view of the astrophysical implications of the gravitomagnetic clock effect around Kerr black holes.

Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations

Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations

Internal dissipation in the Dzhanibekov effect

The Dzhanibekov effect is the phenomenon by which triaxial objects like a spinning wing bolt may continuously flip their rotational axis when initially spinning around the intermediate axis of inertia. This effect is closely related to the Tennis Racket theorem that establishes that the intermediate axis of inertia is unstable. Over time, however, dissipation ensures that a torque free spinning body will eventually rotate around its major axis, in a process called precession relaxation, which counteracts the Dzhanibekov effect. Euler’s equations for a rigid body effectively describe the Dzhanibekov effect, but cannot account for the precession relaxation effect. A dissipative generalization of Euler’s equations displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show through numerical simulations of the dissipative Euler’s equations that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the Dzhanibekov effect.

Quantum field theory, worldline theory, and spin magnitude change in orbital evolution

A previous paper [Z. Bern , Binary dynamics through the fifth power of spin at O(G2), ] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through O(α2) and O(S2), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity. Published by the American Physical Society 2024

Investigation of a Wind Tunnel System for Spinning Body Using Magnetic Suspension

Investigation of a Wind Tunnel System for Spinning Body Using Magnetic Suspension

Geomagnetic Data-based Rotational Speed Measurement Method for High-speed Spinning Bodies

Geomagnetic Data-based Rotational Speed Measurement Method for High-speed Spinning Bodies

High-performance, Wind-driven Triboelectric-Electromagnetic Hybrid Nanogenerator for Self-powered Wireless Transmission and Wind Speed Sensing in the Internet of Things

Wind energy is becoming more crucial in addressing the scarcity of fossil fuel due to the development of promising technologies like Electromagnetic Generators (EGs), Triboelectric Nanogenerators (TNs), and their hybrid nanogenerators. However, only a portion of wind energy can be efficiently converted into electricity. By integrating 5G technology with the Internet of Things (IoT) and expanding the deployment of wireless sensor networks, vulnerable areas may be effectively monitored for potential disasters. Nevertheless, substituting conventional chemical batteries with new ones in IoT devices poses a substantial difficulty, particularly in distant regions. This article presents a hybrid energy harvester explicitly designed for wind energy harvesting. This work introduces the High Performance, Wind-driven Triboelectric-Electromagnetic Hybrid Nanogenerator (HPW-TEHN) as a solution for self-powered Wireless Transmission (WT) and Wind Speed Sensing (WSS) in the Internet of Things (IoT). Here, we present a High-Performance Wind Turbine with a wide operational range of wind speeds, allowing for efficient harnessing of wind energy across different levels, including gentle breezes and moderate and severe winds. The gadget comprises a spinning body and a sliding body. The power-producing mechanism consists of the EGs in the rotating body and the TNs in the sliding body. All created units are fully enclosed within the device box, effectively insulated from challenging environmental conditions. This research comprehensively analyzes the impact of dielectric material kinds and sizes on the output performance of TNs. Additionally, it investigates the output performance of this device under various wind speeds. The performance of HPW-TEHN improves as the wind speed increases. At a wind speed of 10 m/s, the TN, EG, and HPW-TEHN generate an output power of 0.19 mW, 0.38 mW, and 1.4 mW, respectively.

The role of thermal fluctuations in the motion of a free body

The motion of a rigid body is described in Classical Mechanics with the venerable Euler’s equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however, cannot satisfy this property, as a consequence of thermal fluctuations. We generalize Euler’s equations for a free body in order to describe dissipative and thermal fluctuation effects in a thermodynamically consistent way. The origin of these effects is internal, i.e. not due to an external thermal bath. The stochastic differential equations governing the orientation and central moments of the body are derived from first principles through the theory of coarse-graining. Within this theory, Euler’s equations emerge as the reversible part of the dynamics. For the irreversible part, we identify two distinct dissipative mechanisms; one associated with diffusion of the orientation, whose origin lies in the difference between the spin velocity and the angular velocity, and one associated with the damping of dilations, i.e. inelasticity. We show that a deformable body with zero angular momentum will explore uniformly, through thermal fluctuations, all possible orientations. When the body spins, the equations describe the evolution towards the alignment of the body’s major principal axis with the angular momentum vector. In this alignment process, the body increases its temperature. We demonstrate that the origin of the alignment process is not inelasticity but rather orientational diffusion. The theory also predicts the equilibrium shape of a spinning body.

Utilising Magnus Effect to Increase Downforce in Motorsport

The Magnus effect is the generation of a sidewise force on a spinning cylindrical or spherical solid immersed in a fluid (liquid or gas) when there is relative motion between the spinning body and the fluid. This is most commonly seen in baseball, tennis, or European football where the ball’s trajectory is curved due to its rotation. The idea of using the Magnus effect in an airfoil to produce lift was proposed in 1941 in a patent application by Massey. This is also known as Kutta–Joukowski lift, first analyzed by Kutta and Joulowski in the late 19th century. In maritime applications, it is known as Flettner rotor sails, first used in the 1920's. Although Magnus effect is not new, the idea of using it on a racecar wing to improve downforce has not been extensively studied. The concept is to replace the front leading-edge of the wing with a rotating cylinder of the same diameter to produce additional circulation around the foil. This idea was born out of discussion at San Jose State University’s Formula SAE team as a way to create variable downforce on their wings. Although the idea was proposed but it was never built because of the complexity in the construction and a lack of rigorous analysis. Subsequently from our CFD simulation, it shows that by imposing a +2U angular velocity to the front LE cap (i.e., rotating upwards in the negative-x direction), we could gain 4.25% of downforce. Since the leading edge cap is roughly cylindrical, physically replacing it by a cylinder would not cause a visible change to the race car’s geometry while improving the aerodynamics using Magnus effect. This CFD data show promise to take the next step of building a physical prototype and perform aerodynamic experiments to validate this finding. Keywords: Magnus effect, aerodynamics, downforce, CFD, motorsport.

Gravitational Faraday effect from on-shell amplitudes

Effects of massive object’s spin on massive-massless 2 → 2 classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter λ/b, where λ is the massless particle’s wavelength and b is the impact parameter. Corrections in λ/b start to appear from mathcal{O} (G2), with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to mathcal{O} (G2) and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin [1] is reproduced by λ/b correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed [2–8], along with the associated shift symmetry [7], and argue that it holds to arbitrary spin order at mathcal{O} (G2) in the massless probe limit.

Unsteady mixed convective radiative nanofluid flow in the stagnation point region of a revolving sphere considering the influence of nanoparticles diameter and nanolayer

Numerous technological applications, including rotating equipment design, missile re-entry, projectile motion and fiber coating, depend on the rotational flows and heat transfer characteristics of a forced flow stream over stationary spinning bodies of revolution. In this regard, the authors have presented an analytical solution of the mixed convective, time-dependent, laminar, and incompressible MHD flow of a water-based Al2O3 nanofluid towards the stagnation region of an angularly revolving sphere. The nanofluid transport is treated as axisymmetric and possesses constant thermophysical features except for the variation in density which originates the buoyancy force. The analytical solution of this analysis has been attempted by the homotopic approach. The convergence of the homotopic approach is presented with the help of Figure. The impacts of the embedded factors on the flow profiles are presented with the help of Figures and Tables. The results showed that the velocities and thermal profiles of the water-based Al2O3 nanofluid have been significantly enhanced by the volume fraction of an Al2O3 nanoparticle. The increasing nanoparticle diameter declines the thermal scenario while the nonlinear thermal radiation parameter and ratio of the liquid and nanolayer conductivity are enhanced the thermal profiles of the water-based Al2O3 nanofluid.

Spinning test body orbiting around a Kerr black hole: Comparing spin supplementary conditions for circular equatorial orbits

The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon (MPD) equations when its centroid, i.e. its center of mass, is fixed by a Spin Supplementary Condition (SSC). In the present study, we continue the exploration of shifts between different centroids started in a recently published work [ Phys. Rev. D 104, 024042 (2021)], henceforth Paper I, for the Schwarzschild spacetime, by examining the frequencies of circular equatorial orbits under a change of the SSC in the Kerr spacetime. In particular, we examine the convergence in the terms of the prograde and retrograde orbital frequencies, when these frequencies are expanded in power series of the spin measure and the centroid of the body is shifted from the Mathisson-Pirani or the Ohashi-Kyrian-Semerak frame to the Tulczyjew-Dixon one. Since in Paper I, we have seen that the innermost stable circular orbits (ISCOs) hold a special place in this comparison process, we focus on them rigorously in this work. We introduce a novel method of finding ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the Mathisson-Pirani formalisms. We resort to numerical investigation of the convergence between the SSCs for the ISCO case, due to technical difficulties not allowing Paper's I analytical treatment. Our conclusion, as in Paper I, is that there appears to be a convergence in the power series of the frequencies between the SSCs, which is improved when the proper shifts are taken into account, but there exists a limit in this convergence due to the fact that in the spinning body approximation we consider only the first two lower multipoles of the extended body and ignore all the higher ones.

Precisely computing bound orbits of spinning bodies around black holes. I. General framework and results for nearly equatorial orbits

Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Accurate models of such systems require postgeodesic corrections to this motion. Postgeodesic effects that drive the small body away from the geodesic include the gravitational self-force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics (in a sense that can be made precise) and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is $\mathcal{O}(S)$ out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits, contrasting them with geodesics, and show how the small body's spin shifts the frequencies ${\mathrm{\ensuremath{\Omega}}}_{r}$ and ${\mathrm{\ensuremath{\Omega}}}_{\ensuremath{\phi}}$ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations.

Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory.

Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse Δp_{i}^{μ} and spin kick Δa_{i}^{μ} from a scattering of two arbitrarily oriented spinning massive bodies (black holes or neutron stars) in a weak gravitational background up to third post-Minkowskian (PM) order (G^{3}). Two-loop Feynman integrals are performed in the potential region, yielding conservative results. For spins aligned to the orbital angular momentum we find a conservative scattering angle that is fully consistent with state-of-the-art post-Newtonian results. Using the 2PM radiated angular momentum previously obtained by Plefka, Steinhoff, and the present authors, we generalize the angle to include radiation-reaction effects, in which case it avoids divergences in the high-energy limit.

Spin-orbit effects for compact binaries in scalar-tensor gravity

Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However, spin effects are still relatively unexplored in this context. In this work, we construct an effective point-particle action for a generic spinning body that can couple both conformally and disformally to a real scalar field, and we show that requiring the existence of a self-consistent solution automatically implies that if a scalar couples to the mass of a body, then it must also couple to its spin. We then use well-established effective field theory techniques to conduct a comprehensive study of spin-orbit effects in binary systems to leading order in the post-Newtonian (PN) expansion. Focusing on quasicircular nonprecessing binaries for simplicity, we systematically compute all key quantities, including the conservative potential, the orbital binding energy, the radiated power, and the gravitational-wave phase. We show that depending on how strongly each member of the binary couples to the scalar, the spin-orbit effects that are due to a conformal coupling first enter into the phase at either 0.5 PN or 1.5 PN order, while those that arise from a disformal coupling start at either 3.5 PN or 4.5 PN order. This suppression by additional PN orders notwithstanding, we find that the disformal spin-orbit terms can actually dominate over their conformal counterparts due to an enhancement by a large prefactor. Accordingly, our results suggest that upcoming gravitational-wave detectors could be sensitive to disformal spin-orbit effects in double neutron star binaries if at least one of the two bodies is sufficiently scalarised.

A thermal conductivity model for hybrid heat and mass transfer investigation of single and multi-wall carbon nano-tubes flow induced by a spinning body

The enhancement of thermal heat transfer utilizing the hybrid nanofluids is explored widely by numerous researchers over the years. Because of these exciting characteristics features of hybrid nanofluids, the prime focus of this article is the investigation of engine oil and mineral oil-based hybrid nanofluids consisting of carbon nanotubes (SWCNT-MWCNT) over a rotating cone present in a convectively heated permeable environment. In the flow supposition, a mathematical model is formulated, Boundary layer approximations are used to minimize the structure of partial differential equations. The dimensionless system of highly non-linear partial differential equations is obtained through boundary layer approximation. The findings obtained showed a rise in temperature for both CNT's, the thickness of the thermal boundary layer has increased under the impact of solid volume fraction of nanotubes. SWCNTs provide a reduction in skin friction and enhancement in Nusselt number. The hybrid nanofluid with EO (engine oil) base has demonstrated a greater heat transfer coefficient and reduced fluid motion's skin friction than MO (mineral oil) based. The model hybrid flow can be used in industries like turbine heat production, wind energy generation, and pharmaceutical processes.

Spinning test body orbiting around a Schwarzschild black hole: Comparing spin supplementary conditions for circular equatorial orbits

The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of an extended test body in general relativity. This system of equations, though, is underdetermined and has to be accompanied by constraining supplementary conditions, even in its simplest version, which is the pole-dipole approximation corresponding to a spinning test body. In particular, imposing a spin supplementary condition (SSC) fixes the center of mass of the spinning body, i.e., the centroid of the body. In the present study, we examine whether characteristic features of the centroid of a spinning test body, moving in a circular equatorial orbit around a massive black hole, are preserved under the transition to another centroid of the same physical body, governed by a different SSC. For this purpose, we establish an analytical algorithm for deriving the orbital frequency of a spinning body, moving in the background of an arbitrary, stationary, axisymmetric spacetime with reflection symmetry, for the Tulczyjew-Dixon, the Mathisson-Pirani, and the Ohashi-Kyrian-Semer\'ak SSCs. Then, we focus on the Schwarzschild black hole background, and a power series expansion method is developed in order to investigate the discrepancies in the orbital frequencies expanded in power series of the spin among the different SSCs. Lastly, by employing the fact that the position of the centroid and the measure of the spin alters under the centroid's transition, we impose proper corrections to the power expansion of the orbital frequencies, which allows to improve the convergence between the SSCs. Our concluding argument is that when we shift from one circular equatorial orbit to another in the Schwarzschild background, under the change of a SSC, the convergence between the SSCs holds only up to certain powers in the spin expansion, and it cannot be achieved for the whole power series.