General Equations Of Motion Research Articles

Equation of spin motion for a particle with electric and magnetic charges and dipole moments

The general classical equation of spin motion is rigorously derived for a particle with electric and magnetic charges and electric and magnetic dipole moments in electromagnetic fields. The equation describing the spin motion relative to the momentum direction in storage rings is also obtained. The importance of the derivation follows from the potential presence of magnetic charges and EDMs due to the pseudoscalar CP-violating electromagnetic interaction caused by dark matter axions.

New non-supersymmetric flux vacua from generalised calibrations

We construct a new class of non-supersymmetric ten-dimensional type II flux vacua, by studying first order differential equations which are deformations of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions. We do so within the context of Generalised Complex Geometry, where there is a natural interpretation of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions in terms of calibration conditions for probe D-branes, called D-string, domain-wall or space-filling branes, depending on them wrapping two, three or four non-compact dimensions. We focus on the class of non-supersymmetric vacua violating the D-string calibration condition, and write down their general equations of motion in the language of pure spinors. We solve them for a subclass of vacua, where the deformation of the calibration condition is dictated by the foliated geometry of the internal space. We also construct backgrounds violating both the domain-wall and D-string calibration conditions, generalising the one-parameter DWSB class of backgrounds introduced in Lüst et al. We present several explicit solutions with SU(2) and SU(3) structures, and we investigate briefly their associated low energy effective theories.

Frequency Regulation in Nanocomposite Sandwich Joined Conical-Conical Shells with Open Cell Foam Partially Supported by Pasternak Elastic Foundation Using GDQ

This study investigated the natural vibration of a sandwich conical-conical shell that is partially supported by Winkler–Pasternak foundations. The sandwich system comprises an open-cell foam (OCF) core and laminated composite face sheets reinforced with graphene platelets using functionally graded models (FG-GPLRC). To account for through-the-thickness shear deformations and rotary inertias, the first-order theory of shells is combined with Donnell-type kinematic assumptions. Hamilton’s principle is utilized to establish the general motion equations and related boundary and continuity conditions. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature (GDQ) approach. An eigenvalue problem is formulated to analyze the corresponding mode shapes and vibration frequencies for the shell ends and continuity criteria under various boundary conditions. Parametric experiments are conducted for sandwich conical-conical shells partially supported by Winkler–Pasternak foundations. This study examined the impact of multiple factors on the frequency of a joined shell structure, including the total thickness, FG-GPL face sheet thickness, various boundary conditions, the length of each cone segment, and the Winkler and shear elastic foundation. Notably, this research also analyzed the effects of a partial elastic foundation on the structure’s frequency for the first time.

On a Carnot working continuum with non-equilibrium state parameters

We explain that a full description of how the non-equilibrium state of the system evolves in time requires the consideration and solution of its general equation of motion. In the case of the Carnot medium, as a general equation of motion, there must be taken two balances of: nonequilibrium specific volume and non-equilibrium specific entropy. Instead of taking the classical approach where the balance of entropy is postponed to more advanced and theoretical treatments, we focus on the analysis of two, most general, volume and entropy fluxes. These fluxes of motion are universal features of thermodynamics. It has been shown that the Carnot working continuum mathematical model is captured by the two general nonmathematical statements valid for all systems that we call the first law and the second law of thermodynamics.

Non-linear AUV Controller Design Using Logic-Based Switching PID Control

The inspection of pipes without stopping pipeline operations is of industrial interest due to the inherent economic benefits. A pipe inspection robot design is proposed together with a suitable motion controller. The proposed robot is an Autonomous Underwater Vehicle (AUV) architecture that does not require shunting, draining or unearthing pipework for inspection purposes. This posed the challenge of controlling the AUV through a narrow pipe where manouvers are restricted. A set of general non-linear equations of motion were identified and refined using existing research and strip theory. The non-linear analytical model was implemented in Simulink to enable real-time monitoring and controller tuning. A non-linear controller based on a combination of classical PID theory and switching logic was developed to control the platform. The controller was transplanted into a Hardware-in-Loop (HIL) testing model developed with the Arduino and Simulink software suites. Pool tests measuring the parameters pitch and yaw angles showed that when operated independently with a 5° input, the maximum overshoot was 0.5° or 10% of the command value with a maximum angular velocity of 1.25°/s. When operated simultaneously, the overshoot rose to 30% with a constant error in the region of 1° over the target. Distance readings conducted with ultrasonic sensors to the pipe wall showed constant Sway-Heave bias errors from the centerline as −5 mm, and 4 mm, respectively, with an error range of 4 mm / −7 mm for Sway and 6 mm/ −4 mm for Heave. Pitch and heave motions were up to 18% faster than yaw and sway motions due to actuator orientation, with speeds of 6.25°/s and 40.57 mm/s, respectively. Despite the turbulence present during tests, the controller successfully drove the AUV to target positions through active flow and presented a reasonable basis for further refinement.

Gravitoelectromagnetic Field Strength Tensor in Flat Spacetime Frame: Dynamics of a Gyroscope in the Earth’s Gravitational Field

In this article, we develop gravitoelectromagnetism (GEM) as a formal relativistic theory of gravitation characterized by a field potential fourvector in a flat (Minkowski) spacetime frame. By reorganizing the Lense-Thirring spacetime metric of linearized general relativity, we have determined the appropriate field potential four-vector and the field strength tensor which generates dynamics in the GEM field. The general covariant equation of motion of the spin four-vector of a gyroscope driven by the GEM field strength tensor provides the expected form of the frame-dragging and geodetic effects after introducing a gyromagnetic ratio η = 4 as an internal dynamical property of the gyroscope.

Quasiclassical theory for antiferromagnetic metals

Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of the magnetic moments. The quasiclassical framework is useful because it separates the quantum effects occurring at length scales comparable to the Fermi wavelength from other length scales, and has successfully been used to study a wide range of phenomena involving both superconductivity and ferromagnetism. Starting from a tight-binding Hamiltonian, we develop general quasiclassical equations of motion and boundary conditions, which can be used to describe two-sublattice metallic antiferromagnets in the dirty limit. The boundary conditions are applicable also for spin-active boundaries that can be either compensated or uncompensated. Additionally, we show how nonuniform or dynamic magnetic textures influence the equations and we derive a general expression for observables within this framework.

Friedmann equations and cosmic bounce in a modified cosmological scenario

In this work we present a derivation of modified Raychaudhuri and Friedmann equations from a phenomenological model of quantum gravity based on the thermodynamics of spacetime. Starting from general gravitational equations of motion which encode low-energy quantum gravity effects, we found its particular solution for homogeneous and isotropic universes with standard matter content, obtaining a modified Raychaudhuri equation. Then, we imposed local energy conservation and used a perturbative treatment to derive a modified Friedmann equation. The modified evolution in the early universe we obtained suggests a replacement of the Big Bang singularity by a regular bounce. Lastly, we also briefly discuss the range of validity of the perturbative approach and its results.

Nonlinear finite element analysis for seismic site amplification assessment of urban slopes showing surface geology and topography irregularities

In urban areas, buildings close to the crest of a slope can undergo serious seismic disturbances due to seismic site amplifications, often induced by local site conditions. In this context, this paper aims to assess how combined surface geology and topography irregularities can amplify the site response to the ground surface of the Ciloc slope, subject to the reference earthquake that occurred in Constantine province on October 27, 1985. Therefore, a two-dimensional nonlinear dynamic finite element analysis was conducted on various geometric models, in which both slope angle and lithology were simultaneously varied. To describe properly the earthquake frequency content, an analytical solution based on the interpolation method of the general equation of the dynamic motion was programmed under MATLAB language. Fast Fourier Transform (FFT) was also programmed to compute the Fourier spectral amplitude of a selected accelerogramme. Likewise, the computer software SeismoSignal has been used to compare analytical outcomes. Four slope configurations were simulated namely, an actual slope, a layered slope, a homogeneous marl slope and a homogeneous alluvial slope with various slope angles. It was found that maximum site amplifications had occurred behind the crest and not at the exact crest of the slope as commonly expected. Due to the dilatancy phenomenon, alluvial homogenous formations as cohesionless soils, show high spectral parameter amplifications than the other cases. It was also concluded that a seismic response analysis of these sedimentary deposits is strongly recommended as a preliminary study for the seismic analysis of the neighbouring buildings, to avoid serious seismic destructions.

A study of the aerodynamic properties of cotton fiber in the confusor tube of a rotor spinning machine

In this article, the movement of fibers in the air channel and the rotor in the rotor spinning machine was studied. In the experimental work, the uniformity and stability of the velocity field of each channel for moving fibers in an aerodynamic device were checked. In this case, the airflow speed was changed from 5 m/s to 30 m/s. Also, differential equations of motion along the OX and OY axes were created taking into account the air resistance. When determining the movement of fibers in a conical channel, the total speed was divided into components, constant values were found, and general equations of motion were derived.

О влиянии на форму брахистохроны эффекта Магнуса

This paper studies the effect of the rotational motion of a body on the trajectory of its fastest descent into the gravity field. The body is considered as a ball rotating about its instantaneous axis, which is perpendicular to the pattern, with a variable angular frequency. The rotation of the ball creates a vortex flow that induces the highest pressure at the top of the ball and the least pressure at the bottom. Thus, the Magnus force (down-force), which is opposed to the reaction force of a trough, occurs. It provides an "antilifting" effect resulting in strong changes in the brachistochrone shape. Based on the fundamental principle of dynamics, a general vector equation of motion is obtained in the form of projections on a moving basis represented as unit vectors of the tangent and normal to the trajectory of the motion. A parametric solution to the equations describing the shape of the trough in Cartesian coordinates is obtained in the absence of dissipative forces. It follows from the resulting solution that the Magnus effect is most noticeable only for massive bodies of long radius. Using the numerical integration methods, various shapes of the deformed brachistochrone are presented as a result of the Magnus effect

An Alternative Form of the Equation of Motion for Constrained Structural and Mechanical Systems With Singular Mass Matrices

Abstract This paper develops an alternative description of the general equation of motion for constrained mechanical systems with singular mass matrices. The formulation gives a new explicit equation of motion for such systems and provides a simple and elegant way to interpret the manner in which Nature orchestrates constrained motion, something that was not possible for such systems in the past.

Bivariational time-dependent wave functions with biorthogonal adaptive basis sets: General formulation and regularization of equations of motion through polar decomposition.

We derive general bivariational equations of motion (EOMs) for time-dependent wave functions with biorthogonal time-dependent basis sets. The time-dependent basis functions are linearly parameterized and their fully variational time evolution is ensured by solving a set of so-called constraint equations, which we derive for arbitrary wave function expansions. The formalism allows division of the basis set into an active basis and a secondary basis, ensuring a flexible and compact wave function. We show how the EOMs specialize to a few common wave function forms, including coupled cluster and linearly expanded wave functions. It is demonstrated, for the first time, that the propagation of such wave functions is not unconditionally stable when a secondary basis is employed. The main signature of the instability is a strong increase in non-orthogonality, which eventually causes the calculation to fail; specifically, the biorthogonal active bra and ket bases tend toward spanning different spaces. Although formally allowed, this causes severe numerical issues. We identify the source of this problem by reparametrizing the time-dependent basis set through polar decomposition. Subsequent analysis allows us to remove the instability by setting appropriate matrix elements to zero. Although this solution is not fully variational, we find essentially no deviation in terms of autocorrelation functions relative to the variational formulation. We expect that the results presented here will be useful for the formal analysis of bivariational time-dependent wave functions for electronic and nuclear dynamics in general and for the practical implementation of time-dependent CC wave functions in particular.

General time-dependent configuration-interaction singles. I. Molecular case

We present a grid-based implementation of the time-dependent configuration-interaction singles method suitable for computing the strong-field ionization of small gas-phase molecules. After outlining the general equations of motion used in our treatment of this method, we present example calculations of strong-field ionization of helium, lithium hydride, water, and ethylene that demonstrate the utility of our implementation. The following companion paper specializes to the case of spherical symmetry, which is applied to various atoms.

A Robust Controller Design for Simple Robotic Human Arm

Nowadays, the manipulator of two degrees of freedom (2DOF) has many applications. One is a human arm that may be utilized in robotic rehabilitation. The 2DOF controlled robot manipulator usually acts like human arms. This paper aims to design a robust, stable controller for the upper limb robotic model. A sliding mode control (SMC) approach is proposed to realize stability, tracing accuracy, and robustness for 2DOF robotic manipulator. Based on the general manipulator equation of motion, two SMCs are designed. The first is designed according to the input–output stability constraints. The second is designed according to the adaptive law. Not only the trajectory tracking is guaranteed but also stability is ensured. The stability of the controllers is examined based on Lyapunov stability criteria. The controllers and the robotic arm are formulated analytically. The MATLAB platform is adopted to examine and validate the proposed controller’s performance. The addition of adaptation law in the SMC scheme improves the results for the two designed controllers and shows remarkable trajectory tracking and system stability as well. The improvement rate shows an enhancement of 40.5% and 36.7% for manipulator joints 1 and 2, respectively.

Hamiltonian formulation of the stochastic surface wave problem

We devise a stochastic Hamiltonian formulation of the water wave problem. This stochastic representation is built within the framework of the modelling under location uncertainty. Starting from restriction to the free surface of the general stochastic fluid motion equations, we show how one can naturally deduce Hamiltonian structure under a small noise assumption. Moreover, as in the classical water wave theory, the non-local Dirichlet–Neumann operator appears explicitly in the energy functional. This, in particular, allows us, in the same way as in deterministic setting, to conduct systematic approximations of the Dirichlet–Neumann operator and to infer different simplified wave models including noise in a natural way.

Attempt to obtain the general relativistic planet's motion by special relativity techniques

AbstractIt is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined. When the motion thus examined are compared with the one obtained by the general relativity theory in post‐Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.

Vortex Pairs and Dipoles on Closed Surfaces

We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global circulations which is coupled to the dynamics of the vortices is carefully taken into account. Much emphasis is put to the study of vortex pairs, having the Kimura conjecture in focus. This says that vortex pairs move, in the dipole limit, along geodesic curves, and proofs for it have previously been given by S. Boatto and J. Koiller by using Gaussian geodesic coordinates. In the present paper, we reach the same conclusion by following a slightly different route, leading directly to the geodesic equation with a reparametrized time variable. In a final section, we explain how vortex motion in planar domains can be seen as a special case of vortex motion on closed surfaces.

Influence of Shear Effects on the Characteristics of Axisymmetric Wave Propagation in a Buried Fluid-Filled Pipe

The acoustic propagation characteristics of axisymmetric waves have been widely used in leak detection of fluid-filled pipes. The related acoustic methods and equipment are gradually coming to the market, but their theoretical research obviously lags behind the field practice, which seriously restricts the breakthrough and innovation of this technology. Based on the fully three-dimensional effect of the surrounding medium, a coupled motion equation of axisymmetric wave of buried liquid-filled pipes is derived in detail, a contact coefficient is used to express the coupling strength between surrounding medium and pipe, then, a general equation of motion was derived which contain the pipe soil lubrication contact, pipe soil compact contact and pipe in water and air. Finally, the corresponding numerical calculation model is established and solved used numerical method. The shear effects of the surrounding medium and the shear effects at the interface between surrounding medium and pipe are discussed in detail. The output indicates that the surrounding medium is to add mass to the pipe wall, but the shear effect is to add stiffness. With the consideration of the contact strength between the pipe and the medium, the additional mass and the pipe wall will resonate at a specific frequency, resulting in a significant increase in the radiation wave to the surrounding medium. The research contents have great guiding effect on the theory of acoustic wave propagation and the engineering application of leak detection technology in the buried pipe.

Nonlinear Vibration Movements of the Mid-Supported Micro-Beam

This study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies ([Formula: see text]) and nonlinear correction effect parameters ([Formula: see text]) with the progress of the center support position gradually towards [Formula: see text] and the increase of the microbeam elasticity coefficient ([Formula: see text]).