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The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure joints. This novel one-degree-of-freedom zero-force mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former typically stores 6 times less angular momentum and kinetic energy for the same mass while typically occupying 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the stored kinetic energy versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model. [ABSTRACT FROM AUTHOR]

The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 s u (2) -group states) and even and odd Schrödinger cat states related to the other representation of s u (2) -algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the s u (2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C 2 and C 3 . Also, their use in quantum information and computing is mentioned. [ABSTRACT FROM AUTHOR]

Since the 1970s, astronomers have struggled with the issue of how matter can be accreted to promote black-hole growth. While low-angular-momentum stars may be devoured by a black hole, they are not a sustainable source of fuel. Gas, which could potentially provide an abundant fuel source, presents another challenge due to its enormous angular momentum. While viscous torques are not significant, gas is subject to gravity torques from non-axisymmetric potentials such as bars and spirals. Primary bars can exchange angular momentum with the gas within corotation, causing it to spiral inwards until reaching the inner Lindblad resonance. An embedded nuclear bar can then take over. As the gas reaches the black hole's sphere of influence, the torque becomes negative, fueling the center. Dynamical friction also accelerates the infall of gas clouds closer to the nucleus. However, because of the Eddington limit, growing a black hole from a stellar-mass seed is a slow process. The existence of very massive black holes in the early universe remains a puzzle that could potentially be solved through direct collapse of massive clouds into black holes or super-Eddington accretion. [ABSTRACT FROM AUTHOR]

Featured Application: This study is a first step for real-time monitoring the risk of falls during gait. The goal of this study was to analyze instability during stepping at different speeds in young and older adults. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25 y.o. [19–29]) and 15 older adults (68.7 y.o. [63–77]) volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody system with 19 segments, 18 joints and 42 degrees of freedom. They were asked to perform a series of stepping tasks at fast and spontaneous speeds. The stepping was divided into five phases, with successive swing and double-stance phases. Greater instability was observed during the swing phases. The distances reveal a significant higher instability at fast speed for both groups (p < 0.001) for all the phases compared with spontaneous speeds. The anteroposterior distance was significantly greater for older adults, highlighting greater instability compared to young adults, while no differences were observed for the mediolateral distance all along the five phases, suggesting higher risks of backward and forward falls during stepping. [ABSTRACT FROM AUTHOR]

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively. [ABSTRACT FROM AUTHOR]

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a 'rubble pile' volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the 'rubble pile' parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid's surface. Afterwards, the aforementioned 'solidified plug' (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid's surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid's rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid's mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned 'solidified plug', considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum. [ABSTRACT FROM AUTHOR]

Biped robots swing their legs alternately to achieve highly dynamic walking, which is the basic ability required for them to perform tasks. However, swinging of the swinging leg in the air will disturb the interaction between the supporting leg and the ground and affect the upper body's balance during dynamic walking. To allow the robot to use its own intrinsic motion characteristics to maintain stable movement like a human when its lower limbs are affected by unknown disturbances during dynamic walking, the ability to use its arms to resist disturbances is essential. This article presents a hybrid momentum compensation control method for torque-controlled biped robots to adapt to unknown disturbances during dynamic walking. First, a hybrid angular momentum and linear momentum regulator is designed to compensate for the disturbance caused by the swinging leg. Second, based on real-time dynamic state changes of the legs, a mixed-momentum quadratic programming controller is designed to realize stable dynamic walking. The proposed method allows the force-controlled robot to maintain its balance while walking down an unknown platform, and it maintains good straightness in the forward direction of dynamic motion. The proposed method's effectiveness is verified experimentally on the BHR-B2 force-controlled biped robot platform. [ABSTRACT FROM AUTHOR]

Based on the Richards-Wolf (RW) formalism, we obtain two different exact expressions for the angular momentum (AM) density of light in the focus of an optical vortex with a topological charge n and right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value in the focus for an arbitrary integer n. Another expression for the AM density is equal to a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM) and, in the focus of a considered light field, is equal to zero at n = −1. These expressions are not equal at each point in space, but their 3D integrals are equal. Thus, we derive exact expressions for the AM, SAM and OAM densities in the focus of an optical vortex with right circular polarization and demonstrate that the identity for the densities AM = SAM + OAM is not valid. In addition, we show that the expressions for the strength vectors of the electric and magnetic field near the tight focus, obtained on the basis of the RW formalism, are exact solutions of Maxwell's equations. Thus, the RW theory exactly describes the behavior of light near the tight focus in free space. [ABSTRACT FROM AUTHOR]

Based on the novel prescription for the power function, (x + i y) m , the new expression for Ψ (x , y | m) , the eigenfunction of the operator of the third component of the angular momentum, M ^ z , is presented. These functions are normalizable, single valued and, distinct to the traditional presentation, (x + i y) m = ρ m e i m ϕ , are invariant under the rotations at 2 π for any, not necessarily integer, m—the eigenvalue of M ^ z . For any real m the functions Ψ (x , y | m) form an orthonormal set, therefore they may serve as a quantum mechanical eigenfunction of M ^ z . The eigenfunctions and eigenvalues of the angular momentum operator squared, M ^ 2 , derived for the two different prescriptions for the square root, (m 2) 1 / 2 , (m 2) 1 / 2 = | m | and (m 2) 1 / 2 = ± m , are reported. The normalizable eigenfunctions of M ^ 2 are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. It is shown that the purely integer spectrum is not the most general solution but is just the artifact of a particular choice of the Legendre functions as the pair of linearly independent solutions of the eigenvalue problem for the M ^ 2 . [ABSTRACT FROM AUTHOR]

In this paper, we propose an angular momentum-based advection technique that can express the turbulent foam effect. The motion of foam particles, which are strongly bound to the motion of the underlying fluid, is viscous, and sometimes clumping problems occur. This problem is a decisive factor that makes it difficult to express realistic foam effects. Since foam particles, which are secondary effects, depend on the motion of the underlying water, in order to exaggerate the foam effects or express more lively foam effects, it is inevitable to tune the motion of the underlying water and then readjust the foam particles. Because of such a cumbersome process, the readjustment of the foam effects requires a change in the motion of the underlying water, and it is not easy to produce such a scene because the water and foam effects must change at the same time. In this paper, we present a method to maintain angular momentum-based force from water particles without tuning the motion of the underlying water. We can restore the lost turbulent flow by additional advection of foam particles based on this force. In addition, our method can be integrated with screen-space projection frameworks, allowing us to fully embrace all the advantages of this approach. In this paper, the turbulence of the foam particles was improved by minimizing the viscous motion of the foam particles without tuning the motion of the underlying water, and as a result, lively foam effects can be expressed. [ABSTRACT FROM AUTHOR]

The dynamics of spin flips induced by the femtosecond laser are theoretically investigated in this article. The spin flips in this scenario are attributed to the intersystem crossing (ISC) described within the frame of the Rabi model. This new explanation is a step attempting to explain the mechanism of the all-optical magnetic orientation switching in the perspective of the conservation of the angular momentum and breaks of the selection rule, which is ignored in the Raman scattering related explanations. The final spin states discussed herein are closely related to the intensity of the incident laser and the ISC decay rate. The quantitative analysis of the relation between decay rate, temperature and the intensity of the laser is discussed. [ABSTRACT FROM AUTHOR]

This manuscript reveals both the full experimental and methodical details of a most-recent patent that demonstrates a much-desired goal of rotational maneuvers via angular exchange momentum, namely extremely high torque without mathematical singularity and accompanying loss of attitude control while the angular momentum trajectory resides in the mathematical singularity. The paper briefly reviews the most recent literature, and then gives theoretical development for implementing the new control methods described in the patent to compute a non-singular steering command to the angular momentum actuators. The theoretical developments are followed by computer simulations used to verify the theoretical computation methodology, and then laboratory experiments are used for validation on a free-floating hardware simulator. A typical 3/4 CMG array skewed at 54.73° yields 0.15H. Utilizing the proposed singularity penetration techniques, 3H momentum is achieved about yaw, 2H about roll, and 1H about pitch representing performance increases of 1900%, 1233%, and 566% respectfully. [ABSTRACT FROM AUTHOR]

Many extant studies proposed various stabilizing control methods for humanoids during the stance phase while hopping and running. Although these methods contribute to stability during hopping and running, humanoid robots do not swing their legs rapidly during the flight phase to prevent rotation in the yaw direction. Humans utilize their torsos and arms when running to compensate for the angular momentum in the yaw direction generated by leg movement during the flight phase. In this study, we developed an angular momentum control method based on human motion for a humanoid upper body. The method involves calculation of the angular momentum generated by the movement of the humanoid legs and calculation of the torso and arm motions required to compensate for the angular momentum of the legs in the yaw direction. We also developed a humanoid upper-body mechanism having human link length and mass properties, using carbon-fiber-reinforced plastic and a symmetric structure for generating large angular momentum. The humanoid robot developed in this study could generate almost the same angular momentum as that of a human. Furthermore, when suspended in midair, the humanoid robot achieved angular momentum compensation in the yaw direction. [ABSTRACT FROM AUTHOR]

We study numerically the evolution of an expanding system of scalar fields. The initial configuration is non-isotropic and rotating. We calculate the energy-momentum tensor and angular momentum vector of the system. We compare the time scales associated with the isotropization of the transverse and longitudinal pressures, and the decay of the initial angular momentum. We show that even a fairly large initial angular momentum decays significantly faster than the pressure anisotropy.

An astrophysical dynamo converts the kinetic energy of fluids into magnetic energy. Dynamo is a non-local process. Here, we consider whether a dynamo can operate at the magnetopauses of magnetic rapidly rotating planets. We analyze the main necessary condition for the work of this type of dynamo—the rotation transfer from the planet to the magnetopause. We show the role of the current disc around a rapidly rotating magnetic planet in the redistribution of angular momentum depending on the direction of the external magnetic field, using the example of the Jupiter's magnetodisc. [ABSTRACT FROM AUTHOR]

We studied supramolecular chirality induced by circularly polarized light. Photoresponsive azopolymers form a helical intermolecular network. Furthermore, studies on photochemical materials using optical vortex light will also attract attention in the future. In contrast to circularly polarized light carrying spin angular momentum, an optical vortex with a spiral wave front and carrying orbital angular momentum may impart torque upon irradiated materials. In this review, we summarize a few examples, and then theoretically and computationally deduce the differences in spin angular momentum and orbital angular momentum depending on molecular orientation not on, but in, polymer films. UV-vis absorption and circular dichroism (CD) spectra are consequences of electric dipole transition and magnetic dipole transition, respectively. However, the basic effect of vortex light is postulated to originate from quadrupole transition. Therefore, we explored the simulated CD spectra of azo dyes with the aid of conventional density functional theory (DFT) calculations and preliminary theoretical discussions of the transition of CD. Either linearly or circularly polarized UV light causes the trans–cis photoisomerization of azo dyes, leading to anisotropic and/or helically organized methyl orange, respectively, which may be detectable by CD spectroscopy after some technical treatments. Our preliminary theoretical results may be useful for future experiments on the irradiation of UV light under vortex. [ABSTRACT FROM AUTHOR]

A fundamental phenomenon of coherent control is investigated theoretically using the example of neon photoionization by the bichromatic field of a free-electron laser. A system exposed to coherent fields with commensurable frequencies loses some symmetry, which manifests itself in the angular distribution and spin polarization of the electron emission. We predict several such effects, for example, the violation of symmetry with respect to the plane perpendicular to the polarization vector of the second harmonic and the appearance of new components of spin polarization. Furthermore, we predict a very efficient control of spin polarization via manipulation of the phase between the harmonics. Experimental observation of these effects is accessible with modern free-electron lasers operating in the extreme ultraviolet wavelength regime. [ABSTRACT FROM AUTHOR]

An optimization framework for upward jumping motion based on quadratic programming (QP) is proposed in this paper, which can simultaneously consider constraints such as the zero moment point (ZMP), limitation of angular accelerations, and anti-slippage. Our approach comprises two parts: the trajectory generation and real-time control. In the trajectory generation for the launch phase, we discretize the continuous trajectories and assume that the accelerations between the two sampling intervals are constant and transcribe the problem into a nonlinear optimization problem. In the real-time control of the stance phase, the over-constrained control objectives such as the tracking of the center of moment (CoM), angle, and angular momentum, and constraints such as the anti-slippage, ZMP, and limitation of joint acceleration are unified within a framework based on QP optimization. Input angles of the actuated joints are thus obtained through a simple iteration. The simulation result reveals that a successful upward jump to a height of 16.4 cm was achieved, which confirms that the controller fully satisfies all constraints and achieves the control objectives. [ABSTRACT FROM AUTHOR]

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N 1 interacting bosons of mass m 1 driven by a force of amplitude f L , 1 and N 2 interacting bosons of mass m 2 driven by a force of amplitude f L , 2 , is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100 % condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces f L , 1 and f L , 2 . As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed. [ABSTRACT FROM AUTHOR]

Symmetry principles of several distinct kinds are revealingly engaged in an analysis focussing on third harmonic scattering, a current focus of research on nonlinear optics in chiral media. Analysis in terms of irreducible Cartesian tensors elucidates the detailed electrodynamical origin and character of the corresponding material properties. Considerations of fundamental charge, parity and time reversal (CPT) symmetry reveal the conditions for an interplay of transition multipoles to elicit a chiral response using circularly polarised pump radiation, and the symmetry of quantised angular momentum underpins the associated selection rules and angular distribution. The intrinsic structural symmetry of chiral scatterers determines their capacity to exhibit differential response. Exploiting permutational index symmetry in the response tensors enables quantitative assessment of the boundary values for experimentally measurable properties, including circular intensity differentials. [ABSTRACT FROM AUTHOR]

The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam. [ABSTRACT FROM AUTHOR]

The Wigner–Eckart theorem is used for considering the collective effects related to ordering spins in systems of identical particles in ferro- and antiferromagnetic electronic systems, as well as magnetic effects that occur in high spin systems. The Hamiltonian, written in the spin representation in the form obtained by Heisenberg, Dirac, and van Vleck used to describe spin ordering in systems of particles with spin ½, is not appropriate for a description of particle systems with a spin different from ½. "High" spin particles in the spin representation need other forms of the Hamiltonian of the exchange interaction in the spin representation. The Hamiltonian for high-spin particles has been developed from the first principles, and the effects of magnetic ordering in systems of identical particles with arbitrary spin are considered in this review. An effect of giant negative magnetoresistance in the Indium antimonide has been interpreted from the exchange contribution of a high spin heavy holes point of view. [ABSTRACT FROM AUTHOR]

Spiral galaxies are spinning, internally densified objects. The Virial Theorem explains galactic rotation curves via its linkage of the rotation rate to the gravitational self-potential (Ug) and the moment of inertia of oblate spheroids. We devise a new analytical solution that allows galactic mass and volumetric density (kg m−3) profiles to be extracted from velocity and its derivative as functions of equatorial radius. This inverse model of rotation curves is direct, unambiguous, and parameter-free. To probe galactic evolution, we combine energy minimization, angular momentum conservation, and the Virial Theorem. The characteristic flat shape of spiral galaxies results from an initial vertical collapse of a spinning, colossal molecular cloud, which reduces Ug while conserving angular momentum. Subsequent inward densification further lowers Ug, producing bulges, but conserving angular momentum requires mass loss, achieved by the outward movement of the distal parts of the spiral arms. Many of the evolutionary patterns of spiral galaxies are exhibited by the changing shapes of hurricanes during formation and dissipation. In contrast, elliptical galaxies evolve from a cloud with roughly random orbits into progressively rounder, internally denser objects, with angular momentum conserved by the development of vertically oriented jets. Galactic evolution is governed by the initial inventory of mass and angular momentum, resulting in separate paths for elliptical and spiral galaxies, as is codified in Hubble's tuning fork diagram. [ABSTRACT FROM AUTHOR]

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. ψ ˜ = (i c ψ 0 , ψ →) , represents a state of a particle with orbital angular momentum, L = 3 ℏ , resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector ψ → , points in an opposite direction of L → . When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects. [ABSTRACT FROM AUTHOR]