Conservation Of Angular Momentum Research Articles

Relative Motion Estimation Algorithm for Noncooperative Targets Considering Multiple Solutions of Rotational Parameters.

On-orbit servicing using a space robot is gaining popularity among the space community for both economic and safety aspects. In particular, the estimation of the relative motion of a noncooperative target is a challenging problem. This study presents a relative motion estimation scheme based on stereovision for noncooperative targets considering multiple solutions of rotational parameters. Specifically, the mass distribution of the target is identified based on the least-square method and the principle of conservation of angular momentum. Then, the determination of a unique principal axis coordinate frame of the target is employed to resolve the multiple-solution problem. In addition, an EKF (extended Kalman filter)-based filter with global observability is designed to estimate the full motion states and inertia parameters of the target. The convergence performance of the proposed method is verified by numerical simulation. The results also demonstrate that the method is robust to occlusion.

Simulation of Human Movement in Zero Gravity.

In the era of expanding manned space missions, understanding the biomechanical impacts of zero gravity on human movement is pivotal. This study introduces a novel and cost-effective framework that demonstrates the application of Microsoft's Azure Kinect body tracking technology as a motion input generator for subsequent OpenSim simulations in weightlessness. Testing rotations, locomotion, coordination, and martial arts movements, we validate the results' realism under the constraints of angular and linear momentum conservation. While complex, full-body coordination tasks face limitations in a zero gravity environment, our findings suggest possible approaches to device-free exercise routines for astronauts and reveal insights into the feasibility of hand-to-hand combat in space. However, some challenges remain in distinguishing zero gravity effects in the simulations from discrepancies in the captured motion input or forward dynamics calculations, making a comprehensive validation difficult. The paper concludes by highlighting the framework's practical potential for the future of space mission planning and related research endeavors, while also providing recommendations for further refinement.

Indicating the direction in conservation of angular momentum

This study developed a teaching material that makes the conservation of angular momentum, which students find very difficult, more concrete. The fact that angular momentum is a vector concept, the direction of the vector and the importance of this vector direction in angular momentum conservation are visualized. The teaching material consists of a table mounted on a freely rotating shaft, two electric motors mutually connected to the table, and a speed adjuster circuit used to change the rotation speeds of the motors. When electric motors begin to rotate, the angular momentum of the motors changes. How the angular momentum of the system is preserved thanks to the changing angular momentum of the parts interacting with each other, the directions of the vectors formed, the inertia torque, angular velocity, angular momentum relationship, and the relationship of the parts forming a system with each other have been tried to be explained in detail through the teaching material. When the motors were operated in different directions and speeds, the change in the rotation direction of the table was observed. This observation concretizes that angular momentum and angular momentum conservation are vector concepts. The right-hand rule, which describes the angular momentum vector direction with the material, can be demonstrated to students in practice. Video recordings showing how the teaching material works have been shared with readers.

Fluid–rigid body coupling simulations with the passively moving solid model based on a physically consistent particle method

Fluid–rigid body interaction is a significant topic in research on particle methods. This study developed a fluid–rigid body coupling method based on a physically consistent particle method, i.e., the moving particle hydrodynamics (MPH) method, incorporating the passively moving solid (PMS) model. When the discrete particle system satisfies the fundamental laws of physics, i.e., mass conservation, linear and angular momentum conservation, and the second law of thermodynamics, the method is asserted physically consistent, and this feature is important for robust dynamic calculations. The PMS model is a pioneering approach that is practical for particle methods in which fluid and rigid-body particles are initially calculated as a fluid. Then, only rigid-body particles are modified to restore the initial shape by applying rigid-body constraints. Thus, combining the MPH method and the PMS model realizes a fluid–rigid body coupling method that satisfies fundamental physical laws. The proposed method was first verified via the fundamental rigid body and fluid–rigid body coupling problems: the Dzhanibekov effect on a T-shaped rigid body, a floating rectangular solid, a floating cylinder, and water entry of a two-dimensional cylinder. Second, the proposed method was validated via calculating a cylinder rolling on a liquid film as a fluid–rigid body coupling problem with rotation. By using a potential-based surface tension model, the computed results showed reasonable agreement with the experimental data obtained in this study. Overall, it was confirmed that the proposed method is a promising fluid–rigid body coupling approach, in which the surface tension and wettability can be considered as well.

Particle nature of the photonic spin Hall effect.

It is widely recognized that light exhibits a wave-particle duality. However, the explanation for the photonic spin Hall effect (PSHE) primarily relies on the wave nature of light as dictated by Maxwell's Equations. There is a lack of exploration into the particle nature of light in this regard. In this context, we offer a fresh interpretation of the PSHE from the perspective of particle nature of light. For the out-of-plane PSHE, the spin shifts result from the macroscopic manifestation of the conservation of spin-orbital angular momentum of one photon. For the in-plane PSHE, the spin shifts arise from the spread of in-plane wavevector. Based on the wave nature of light, we also obtain the same spin shifts, confirming the consistency of the wave-particle duality of light. Furthermore, we find that the spin shifts of the PSHE are not the overall displacement of photons with the same handedness, but the outcome of coherent superposition among photons of the same handedness. These discoveries further enhance our comprehension of the fundamental nature of the PSHE.

A slowly evolving conical pendulum

The idea of this work originally arose from a question pertaining to a laboratory experiment on circular motion in our departmental lab manual. The experiment itself involves rotating a bob along a horizontal circle (Figure 1), where the tension in the string attached to the bob provides the centripetal acceleration of the bob, the string itself passing through a smooth vertical pipe. It is assumed that the rotation is fast enough for the effect of gravity to be neglected and therefore the orientation of the part of the string between the top end of the pipe and the bob can be taken to be horizontal. The abovementioned question enquires what happens to the speed of the bob in the case that the bottom end of the string is hand-held and pulled slowly so that the radius of the circular orbit decreases. The answer to the question is straightforward. Either a work-energy argument or an argument involving the conservation of angular momentum provides the same correct answer.

Inhomogeneity of the Ideal Gas of a Finite Number of Particles with Angular Momentum Conservation

We continue to study various aspects of the behavior of a classical ideal gas in a stationary axisymmetric container. The symmetry of the vessel leads to the conservation of the gas’s angular momentum and, hence, the state of gas rotation. We consider the case of a nonrotating two-dimensional gas of a finite number of colliding particles. In this case, the gas statistical distributions differ from the classical ones found in the nineteenth century. We will show that the filling of the axisymmetric vessel with a nonrotating gas is not uniform and provide the exact spatial distribution of gas particles. This previously unknown distribution depends on all the particle masses and is found explicitly. The absence of a rotation in gas layers is shown through the investigation of the distributions of the tangential components of particle momenta. We also show that, for any number of particles in a container, the behavior of a massive enough particle may be unusual. The analytic results are confirmed by simple numerical experiments.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using abinitio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.

Synthetic populations of protoplanetary disks: Impact of magnetic fields and radiative transfer

Context. Protostellar disks are the product of angular momentum conservation during protostellar collapse. Understanding their formation is crucial because they are the birthplace of planets and their formation is also tightly related to star formation. Unfortunately, the initial properties of Class 0 disks and their evolution are still poorly constrained both theoretically and observationally. Aims. We aim to better understand the mechanisms that set the statistics of disk properties as well as to study their formation in massive protostellar clumps. We also want to provide the community with synthetic disk populations to better interpret young disk observations. Methods. We used the ramses code to model star and disk formation in massive protostellar clumps with magnetohydrodynamics, including the effect of ambipolar diffusion and radiative transfer as well as stellar radiative feedback. Those simulations, resolved up to the astronomical unit scale, have allowed us to investigate the formation of disk populations. Results. Magnetic fields play a crucial role in disk formation. A weaker initial field leads to larger and massive disks and weakens the stellar radiative feedback by increasing fragmentation. We find that ambipolar diffusion impacts disk and star formation and leads to very different disk magnetic properties. The stellar radiative feedback also have a strong influence, increasing the temperature and reducing fragmentation. Comparing our disk populations with observations reveals that our models with a mass-to-flux ratio of 10 seems to better reproduce observed disk sizes. This also sheds light on a tension between models and observations for the disk masses. Conclusions. The clump properties and physical modeling significantly impact disk populations. It is critical to for the tension, with respect to disk mass estimates, between observations and models to be solved with synthetic observations. This is particularly important in the context of understanding planet formation.

Spin dynamics in intermediate-energy heavy-ion collisions with rigorous angular momentum conservation

Spin dynamics in intermediate-energy heavy-ion collisions with rigorous angular momentum conservation

ON STABILITY OF SOLITONS FOR MAXWELL–LORENTZ SYSTEM WITH SPINNING PARTICLE

Abstract. We consider stability of solitons of the Maxwell–Lorentz system with extended charged spinning particle. The solitons are solutions which correspond to a particle moving with a constant velocity v with |v| < 1 and rotating with a constant angular velocity ω, [1]–[4]. Our main results are the orbital stability of moving solitons with ω = 0 and a linear orbital stability of rotating solitons with v = 0. The Hamilton–Poisson structure of the Maxwell–Lorentz system is degenerate and admits the Casimir invariants, [1]. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case ω ≠ 0 relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem

Locked differential rotation in core-helium burning red giants

Context. Oscillation modes of a mixed character are able to probe the inner region of evolved low-mass stars and offer access to a range of information, in particular, the mean core rotation. Ensemble asteroseismology observations are then able to provide clear views on the transfer of angular momentum when stars evolve as red giants. Aims. Previous catalogs of core rotation rates in evolved low-mass stars have focussed on hydrogen-shell burning stars. Our aim is to complete the compilation of rotation measurements toward more evolved stages, with a detailed analysis of the mean core rotation in core-helium burning giants. Methods. The asymptotic expansion for dipole mixed modes allows us to fit oscillation spectra of red clump stars and derive their core rotation rates. We used a range of prior seismic analyses, complete with new data, to get statistically significant results. Results. We measured the mean core rotation rates for more than 1500 red clump stars. We find that the evolution of the core rotation rate in core-helium-burning stars scales with the inverse square of the stellar radius, with a small dependence on mass. Conclusions. Assuming the conservation of the global angular momentum, a simple model allows us to infer that the mean core rotation and envelope rotation are necessarily coupled. The coupling mechanism ensures that the differential rotation in core-helium-burning red giants is locked.

Correlated fission fragment angular momenta

Nuclear fission produces fragments whose spins are coupled to each other as well as to the relative fragment motion due to angular momentum conservation. Statistical ensembles of such spins can readily be obtained by either direct microcanonical sampling or by sampling of the associated normal modes of rotation. The spin-spin opening angle distribution is illustrated for both 3D and 2D spin scenarios and it is demonstrated how recent calculations with various models can be well reproduced by the statistical results under different assumptions about the scission geometry.

Toward Development of a Plate Discrete Element Method: Geometry and Kinematics

Shapes of constituent particles have a prominent effect on the macroscopic responses of granular assemblies. Clayey minerals often possess a plate-shaped geometry with a large surface-to-volume ratio. It is difficult to model such a geometry with spheres or clusters of spheres in a conventional discrete element method (DEM). In this study, we present a new DEM for plate-shaped particles with a focus on particle geometry and kinematics. The moment of inertia for a general convex plate is given and unit quaternions are adopted to represent the angular degrees of freedom. In addition, the equation of motion for rotation is proposed to be solved in a body-fixed rather than in a space-fixed reference frame. We present simulations of the rotation of a system of plate-shaped particles under the conservation of angular momentum without external torque. The results demonstrate the necessity and importance of enforcing the unity constraint on the quaternions numerically solved from the equation of motion for rotation.

Propagation of angular momentum in charged pion decay and related processes

There are confusions about angular momentum propagation in scattering or decay processes involving the transition between particle systems that appear to transform differently under Lorentz transformations. This paper provides an analysis of the transformation properties of the states and interactions for a few typical processes within the standard model of particle physics, and performs explicit calculations showing how angular momentum transfers in these processes. We shall show explicitly (a) how a state with zero angular momentum evolves via interactions mediated by a single vector boson of spin one, and (b) that angular momentum conservation is completely consistent with the calculation in quantum field theory. A discussion is also given about the phenomenological consequences of the theoretical results obtained in this study.

Manipulating helical phase of HHG vortex with atomic states

By deploying the strong-field approximation theory, we perform numerical simulation on atomic high-order harmonic generation (HHG) of hydrogen and HHG vortices generated by hydrogen layer. Our results show that the atomic HHG spectra demonstrate peak-shifting and the helical phase of the HHG vortex can be manipulated with initial states of atoms, all ionized by oppositely polarized bicircular ω and 2ω Laguerre–Gaussian fields. The HHG peaks shift to higher frequency by ω if the initial state is switched from ψ100 to ψ211 , and the HHG peaks shift to lower frequency by ω if the initial state is switched from ψ100 to ψ21−1 , the final state is always the ground state ψ100 . The helical phase patterns of the HHG vortices are investigated in connection with the atomic HHG peak-shifting and the angular momentum conservation law. In addition, we observe that the fourth HHG harmonic is strongly dependent on the 2ω field but weakly on the ω field for an initial atomic state of magnetic quantum number −1.

Conservation and non-conservation of photonic angular momentum in a gradient-index fiber

Photonic angular momentum (AM), including the orbital AM (OAM) and spin AM (SAM) of vector vortex beams (VVBs) and partially-coherent VVBs, is analyzed in gradient-index (GRIN) fiber transmission. Photonic spin-orbit interactions (SOIs) occur and the photonic SAM, OAM, and AM (the sum of SAM and OAM) of radially-polarized vortex beams (RVBs) and partially-coherent RVBs (PRVBs) on different planes in the GRIN fiber are simulated. The photonic AM is conserved or not conserved from the SOIs of the RVB and PRVB during GRIN fiber transmission. Simultaneously, the non-conservation characteristics of the photonic AM are regulated by coherence.

Angular Momentum Conserving Limiters for the Euler Equations

Limiters that are used to stabilise the discontinuous Galerkin method fail to preserve its angular momentum conservation property. We propose a simple technique that restores the conservation of angular momentum while preserving the second-order accuracy of the scheme when paired with an explicit time integrator. Numerical experiments confirm the conservation property of the technique paired with two limiters [Giuliani and Krivodonova. 2018. “Analysis of Slope Limiters on Unstructured Triangular Meshes.” Journal of Computational Physics 374: 1–26; Giuliani and Krivodonova. 2019. “A Moment Limiter for the Discontinuous Galerkin Method on Unstructured Triangular Meshes.” SIAM Journal on Scientific Computing 41 (1): A508–A537]. We show that the technique eliminates numerical artifacts that arise from limiting solutions to the Euler equations.

Generation and Manipulation of Spin‐Orbit Coupling mode via Four‐Wave Mixing with Quantum Interference

AbstractRecently, the vectorial nonlinear optical processes driven by spin‐orbit coupling (SOC) light have come to the fore, leading to striking optical phenomena and important applications both in classical and quantum optics. However, research on the SOC‐mediated light‐atom interactions is still in its infancy. Here, the generation and manipulation of SOC mode through a vectorial four‐wave mixing (FWM) process in 85Rb vapor is demonstrated. Under the excitation of two SOC pump beams, multiple FWM paths can be simultaneously established due to the rich atomic Zeeman sublevels coupling with different circularly polarized components of SOC fields. A higher‐order cylindrical or more general SOC FWM signal is observed in the vectorial FWM process, which obeys angular momentum conservation and Gouy phase matching. In particular, quantum interference between different FWM paths plays a crucial role in manipulating the SOC mode of the generated FWM signal, revealing that the conversion of SOC mode is intrinsically quantum. This work provides a pathway toward deeper insight into the vectorial nonlinear optical processes and may advance technology for shaping spatially structured light, which is essential in applications such as nonlinear polarization imaging and the optical communication realm.

Stable Vortex Particle Method Formulation for Meshless Large-Eddy Simulation

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier–Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM.