Showing papers on "Inertia published in 2015"
TL;DR: In this article, a virtual synchronous generator (VSG) with alternating moment of inertia (OMO) was proposed to enhance the response of the virtual machine in tracking the steady-state frequency.
Abstract: The virtual synchronous generator (VSG) is a control scheme applied to the inverter of a distributed generating unit to support power system stability by imitating the behavior of a synchronous machine. The VSG design of our research incorporates the swing equation of a synchronous machine to express a virtual inertia property. Unlike a real synchronous machine, the parameters of the swing equation of the VSG can be controlled in real time to enhance the fast response of the virtual machine in tracking the steady-state frequency. Based on this concept, the VSG with alternating moment of inertia is elaborated in this paper. The damping effect of the alternating inertia scheme is investigated by transient energy analysis. In addition, the performance of the proposed inertia control in stability of nearby machines in power system is addressed. The idea is supported by simulation and experimental results, which indicates remarkable performance in the fast damping of oscillations.
644 citations
TL;DR: In this paper, an improved active power control method for variable speed wind turbine to enhance the inertial response and damping capability during transient events is investigated, which shifts the turbine operating point from the maximum power point tracking (MPPT) curve to the virtual inertia control (VIC) curve according to the frequency deviation.
Abstract: This paper investigates an improved active power control method for variable speed wind turbine to enhance the inertial response and damping capability during transient events. The optimized power point tracking (OPPT) controller, which shifts the turbine operating point from the maximum power point tracking (MPPT) curve to the virtual inertia control (VIC) curves according to the frequency deviation, is proposed to release the “hidden” kinetic energy and provide dynamic frequency support to the grid. The effects of the VIC on power oscillation damping capability are theoretically evaluated. Compared to the conventional supplementary derivative regulator-based inertia control, the proposed control scheme can not only provide fast inertial response, but also increase the system damping capability during transient events. Thus, inertial response and power oscillation damping function can be obtained in a single controller by the proposed OPPT control. A prototype three-machine system containing two synchronous generators and a PMSG-based wind turbine with 31% of wind penetration is tested to validate the proposed control strategy on providing rapid inertial response and enhanced system damping.
282 citations
TL;DR: In this paper, size-dependent equations of motion for functionally graded cylindrical shell were developed using shear deformation model and rotation inertia, where material properties of the shell were assumed as continuously variable along thickness, consistent with the variation in the component's volume fraction based on power law distribution.
191 citations
TL;DR: In this article, the von Karman plate theory is employed to model the system by retaining in-plane displacements and inertia, and the nonlinear dynamics are examined through plotting the frequency-response and force-response curves of the system.
172 citations
TL;DR: In this article, a geometrically imperfect microplate is modelled by means of the von Karman plate theory and Kirchhoff's hypotheses retaining all in-plane and out-of-plane displacements and inertia.
170 citations
TL;DR: In this article, a novel procedure for estimating the total inertia of the Great Britain (GB) power system is presented, where a method is proposed to first detect a suitable event for analysis, and then filter the measured transients in order to obtain a reliable estimate of inertia for a given region of the GB network.
Abstract: A novel procedure for estimating the total inertia of the Great Britain (GB) power system is presented. Following an instantaneous in-feed loss, regional variations in the estimate of inertia are obtained from measured frequency transients using installed synchronised phasor measurement units (PMUs). A method is proposed to first detect a suitable event for analysis, and then filter the measured transients in order to obtain a reliable estimate of inertia for a given region of the GB network. The total inertia for the whole system is then calculated as a summation, with an estimate also provided as to the contribution to inertia from residual sources, namely synchronously connected demand and embedded generation. The approach is first demonstrated on the full dynamic model of the GB transmission system, before results are presented from analyzing the impact of a number of instantaneous transmission in-feed loss events using phase-angle data provided by PMUs from the GB transmission network and also devices installed at the domestic supply at 4 GB universities.
141 citations
TL;DR: In this article, a novel adaptive attitude control scheme for a spacecraft with inertia matrix parameters that have both unknown rigid components and only partially determined variable components is presented. But the proposed controller directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time.
Abstract: Although adaptive control schemes for spacecraft attitude tracking are abundant in controls literature, very few are designed to guarantee consistent performance for a spacecraft with both rigid and nonrigid (time-varying) inertia components. Because inertia matrix changes are a common occurrence due to phenomena like fuel depletion or mass displacement in a deployable spacecraft, an adaptive control algorithm that takes explicit account of such information is of significant interest. In this paper, a novel adaptive attitude control scheme is presented for a spacecraft with inertia matrix parameters that have both unknown rigid components and only partially determined variable components. The proposed controller directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time. For the particular case of an input-dependent inertia matrix, a bounded control solution is ensured by placing some mild restrictions on the initial conditions and by empl...
121 citations
TL;DR: In this article, the optimal inertia placement problem in a linear network-reduced power system model is investigated and a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions are provided.
Abstract: A major transition in the operation of electric power grids is the replacement of synchronous machines by distributed generation connected via power electronic converters. The accompanying "loss of rotational inertia" and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of "where" to place this inertia. It is however strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. In this article, we carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem. We consider a linear network-reduced power system model along with an H2 performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. Further, we also consider the robust inertia allocation problem, wherein the optimization is carried out accounting for the worst-case disturbance location. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.
118 citations
TL;DR: In this paper, the effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters.
Abstract: The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertial effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle focusing.
105 citations
01 Dec 2015
TL;DR: An optimization program is proposed that analytically derive the sensitivities of transient frequency overshoot and damping ratio to inertia and damped, and shows how damping ratios can be improved while transient frequency limits are respected.
Abstract: Rotational Inertia is an integral part of any electric power system. Due to the increased use of power electronics—both to connect Renewable Energy Sources (RES) and as drives for electric motors—inertia levels are generally reduced and become time dependent. The same power electronic technologies can also be used to actively provide inertia to the power system, raising the question what effect changes in inertia has on power system stability, and how to best place devices providing virtual inertia. We propose an optimization program that answers these question, and analytically derive the sensitivities of transient frequency overshoot and damping ratio to inertia and damping. An example shows how damping ratio can be improved while transient frequency limits are respected.
96 citations
TL;DR: In this paper, a multiscale theory of solids based on the concept of representative volume element (RVE) and accounting for micro-scale inertia and body forces is proposed.
TL;DR: This paper proposes a novel algorithm to identify three inertial parameters: sprung mass, yaw moment of inertia, and longitudinal position of the center of gravity using a four-wheel nonlinear vehicle model and a dual unscented Kalman filter.
Abstract: This paper proposes a novel algorithm to identify three inertial parameters: sprung mass, yaw moment of inertia, and longitudinal position of the center of gravity. A four-wheel nonlinear vehicle model with roll dynamics and a correlation between the inertial parameters is used for a dual unscented Kalman filter to simultaneously identify the inertial parameters and the vehicle state. A local observability analysis on the nonlinear vehicle model is used to activate and deactivate different modes of the proposed algorithm. Extensive CarSim simulations and experimental tests show the performance and robustness of the proposed approach on a flat road with a constant tire–road friction coefficient.
TL;DR: The rotational and translational dynamics of oblate spheroidal particles suspended in a directly simulated turbulent channel flow have been examined in this article, where it was shown that the rotational inertia about the symmetry axis of the disk-like particles hampered the spin-up of the flattest particles to match the mean flow vorticity.
Abstract: The translational and rotational dynamics of oblate spheroidal particles suspended in a directly simulated turbulent channel flow have been examined. Inertial disk-like particles exhibited a significant preferential orientation in the plane of the mean shear. The rotational inertia about the symmetry axis of the disk-like particles hampered the spin-up of the flattest particles to match the mean flow vorticity. The influence of the particle shape on the orientation and rotation diminished as the translational inertia increased from Stokes number 1 to 30. An isotropization of both orientation and rotation could be observed in the core region of the channel. The translational motion of the oblate spheroids had a weak dependence on the aspect ratio. We therefore concluded that inertial particles sample nearly the same flow field irrespective of shape. Nevertheless, the orientation and rotation of disk-like particles turned out to be qualitatively different from the dynamics of fibre-like particles.
TL;DR: In this paper, the robust generalized coordinate partitioning (RPCF) algorithm is used to solve the index-one form of the multibody system equations of motion formulated by using the proposed NACF as well as the well-known RPCF.
Abstract: The purpose of this paper was to present the key features of a novel coordinate formulation for the analytical description of the motion of rigid multibody systems, namely the natural absolute coordinate formulation (NACF). As it is shown in this work, the kinematic and dynamic analysis of rigid multibody systems can be significantly enhanced employing the NACF. In particular, this formulation combines the main advantages of the natural coordinate formulation (NCF), such as the remarkable property of leading to a constant mass matrix and to zero centrifugal and Coriolis generalized inertia forces, with the generality and the effectiveness of the reference point coordinate formulation (RPCF), which is essentially represented by the possibility to develop and assemble the equations of motion of a multibody system together with the algebraic equations which model the joint constraints in a systematic manner. Moreover, a new computational method hereinafter referred to as the robust generalized coordinate partitioning algorithm is also introduced in this work. The robust generalized coordinate partitioning algorithm can be successfully utilized to numerically solve the index-one form of the multibody system equations of motion formulated by using the proposed NACF as well as the well-known RPCF. In particular, the computational procedure presented in this paper owes its robustness to the combination of the main ideas of the well-established generalized coordinate partitioning method, which is commonly employed to cope with the drift phenomenon of the constraint equations at the position and velocity levels when an index-one formulation of the equations of motion is considered, with the more general and advanced constraint enforcement technique at the acceleration level represented by the fundamental equations of constrained motion. In fact, the fundamental equations of constrained motion represent an effective and efficient method able to calculate analytically the generalized constraint forces relative to a multibody system subjected to a general set of redundant holonomic and/or nonholonomic constraint equations by using the Gauss principle of least constraint, thus avoiding the definition of the Lagrange multipliers. The fundamental equations of constrained motion are remarkably effective when used for modeling the dynamic behavior of rigid multibody systems mathematically represented employing the NACF, as it is shown in this paper. Four simple benchmark multibody systems are also examined in order to exemplify the application of the principal concepts developed in the paper.
TL;DR: A theoretical framework is introduced that proposes a tentative, but potentially complete, scaling description of stationary flows of hard particles and makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.
Abstract: Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases both for aerial granular flows dominated by inertia and for over-damped suspensions. Concomitantly, the length scale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete, scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies both to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall, we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For overdamped flows, more observations are needed to decide if friction is a relevant perturbation. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.
TL;DR: In this article, it is shown that to each tetrad there is naturally a spin connection that locally removes the inertial effects from the action, and the use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values.
Abstract: In general relativity, inertia and gravitation are both included in the Levi–Civita connection. As a consequence, the gravitational action, as well as the corresponding energy–momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.
TL;DR: In this article, a novel on-line inertia identification method with a load torque observer is presented to optimize the speed loop PID parameters of a servo system. But, the method of speed loop PI parameters optimization with the identified inertia and load torque is deduced in frequency domain.
Abstract: This paper presents a novel on-line inertia identification method with a load torque observer to optimize the speed loop PID parameters of a servo system. The proposed inertia identification algorithm in this paper adopts the fixed-order recursive empirical frequency-domain optimal parameter estimation to improve the speed loop performance. A load torque observer is employed in order to obtain a more precise value of inertia. Then, the method of speed loop PI parameters optimization with the identified inertia and load torque is deduced in frequency domain. Compared with the recursive least square algorithm, the effectiveness of the proposed method is demonstrated by the simulation and experimental results.
TL;DR: In this article, the authors quantitatively measure the evolution of the bottom interface and find that surface tension determines the air film thickness below the first kink, after which fluid is diverted outward to form a second even sharper kink.
Abstract: A liquid drop approaching a solid surface deforms substantially under the influence of the ambient air which needs to be squeezed out before the liquid can actually touch the solid. We use nanometer- and microsecond-resolved dual wavelength interferometry described in Part I (also published in this issue) to reveal the complex spatial and temporal evolution of the squeezed air layer. In low-velocity droplet impact, i.e., We numbers of order unity, the confined air layer below the droplet develops two local minima in thickness. We quantitatively measure the evolution of the droplet bottom interface and find that surface tension determines the air film thickness below the first kink, after which fluid is diverted outward to form a second even sharper kink. Depending on We, one of the two kinks approaches the surface more closely forming liquid-solid contact. The early time spreading of liquid-solid contact is controlled by the capillary driving force and the inertia of the liquid. The cushioned air film geometry, i.e., a flat micrometer-thin gap, induces an increase of the spreading velocity; the contact area first spreads over the cushioned region, only then followed by radial spreading. This spreading mechanism can lead to the entrapment of one or more air bubbles.
TL;DR: In this paper, the energy absorption characteristics of a type of conical tubes with graded thickness (CTGT) under oblique impact loads were investigated numerically by using finite element model validated by experiments.
TL;DR: In this article, the generalized reciprocal theorem and a vector spheroidal harmonics formalism are used to find closed-form analytical expressions for the inertial torque and the viscoelastic torque acting on a sedimenting sphroid of an arbitrary aspect ratio.
Abstract: An axisymmetric particle sedimenting in an otherwise quiescent Newtonian fluid, in the Stokes regime, retains its initial orientation. For the special case of a spheroidal geometry, we examine analytically the effects of weak inertia and viscoelasticity in driving the particle towards an eventual steady orientation independent of initial conditions. The generalized reciprocal theorem, together with a novel vector spheroidal harmonics formalism, is used to find closed-form analytical expressions for the inertial torque and the viscoelastic torque acting on a sedimenting spheroid of an arbitrary aspect ratio. Here, is the Reynolds number, with being the sedimentation velocity, the semi-major axis and the fluid kinematic viscosity, and is a measure of the inertial forces acting at the particle scale. The Deborah number, , is a dimensionless measure of the fluid viscoelasticity, with being the intrinsic relaxation time of the underlying microstructure. The analysis is valid in the limit , and the effects of viscoelasticity are therefore modelled using the constitutive equation of a second-order fluid. The inertial torque always acts to turn the spheroid broadside-on, while the final orientation due to the viscoelastic torque depends on the ratio of the magnitude of the first ( ) to the second normal stress difference ( ), and the sign (tensile or compressive) of . For the usual case of near-equilibrium complex fluids – a positive and dominant ( , and ) – both prolate and oblate spheroids adopt a longside-on orientation. The viscoelastic torque is found to be remarkably sensitive to variations in in the slender-fibre limit ( ), where is the aspect ratio, being the radius of the spheroid (semi-minor axis). The angular dependence of the inertial and viscoelastic torques turn out to be identical, and one may then characterize the long-time orientation of the sedimenting spheroid based solely on a critical value ( ) of the elasticity number, . For , inertia (viscoelasticity) prevails with the spheroid settling broadside-on (longside-on). The analysis shows that for , and the viscoelastic torque thus dominates for a slender rigid fibre. For a slender fibre alone, we also briefly analyse the effects of elasticity on fibre orientation outside the second-order fluid regime.
TL;DR: In this article, the authors investigated the runaway stability criterion by considering all of the important effects in the hydromechanical system, and deduced the stability criterion with analyses of its effects.
Abstract: Pump-turbine characteristics greatly affect the operational stability of pumped-storage plants. In particular, the S-shaped region of the characteristic curves leads to severe instability during runaway conditions with servomotor failure. Thus, this paper aims to investigate the runaway stability criterion by considering all of the important effects in the hydromechanical system. The criterion also helps to judge the S-characteristics of pump-turbines and can provide a guide for plant design and turbine optimization. First, the pump-turbine characteristic curves are locally linearized to obtain formulae for the relative changes of discharge and torque, which depend on the relative changes of rotational speed and water head. Control theory is then applied to analyze the high-order system, by importing the transfer function of the conduits in the elastic mode. Two different kinds of oscillation are found, associated with water inertia and elasticity, based on the established theoretical mathematical model. New stability criteria for the inertia wave in both rigid and elastic modes are developed and compared. The comparison reveals the effect of the water elasticity on runaway instability, which has often been neglected in the previous work. Other effects, such as friction loss and the timescales of water flow and machinery, are also discussed. Furthermore, the elastic wave, which often has a higher frequency than the inertia wave, is also studied. The stability criterion is deduced with analyses of its effects. Based on the stability criteria for the inertia wave and elastic wave, the unstable regions for two waves of the S-shaped curves are plotted. The results are applied to explain the development from inertia wave to elastic wave during transient behavior at runaway conditions. Model tests of runaway conditions were conducted on a model pumped storage station and the experimental data show good agreement with the theoretical analyses regarding the instability of the inertia wave. Further analyses and validations are made based on transient simulations. The simulation software topsys, which uses the method of characteristics (MOC) and a unit boundary represented by a spatial pump-turbine characteristic surface, was applied to analyze the elastic wave. This also supports the conclusions of the theoretical research.
03 Sep 2015
TL;DR: In this article, a PV-hydro system was simulated in MATLAB/Simulink to analyze the transient stability problems due to PV fluctuations and/or load or generation changes.
Abstract: Transient stability of photovoltaic-hydro microgrid systems is poor due to lack of inertia and the intermittent nature of photovoltaic systems. The stability of such systems can be improved by using virtual synchronous machines which add inertia into the system to allow for higher PV penetration without losing stability. A PV-hydro system was simulated in MATLAB/Simulink to analyze the transient stability problems due to PV fluctuations and/or load or generation changes. Virtual synchronous machine was added which reduced the frequency deviations and the high rate of change of frequency. The results indicate that the transient stability of photovoltaic-hydro microgrid systems can be improved by using virtual synchronous machines using a minimum amount of energy storage. However, the power requirements of the virtual synchronous machine's converter was found to be high compared to the overall system size. Furthermore, high PV penetration levels were achieved by adding virtual synchronous machine to the system.
TL;DR: In this paper, a numerical study on the hydrodynamics of bottom-hinged plate wave energy converters in regular and irregular waves is presented, where a parametric analysis of the plate width and height is performed.
TL;DR: In this article, a semi-passive energy extraction system considering inertial effects is considered and the incompressible Navier-Stokes equations are solved using a finite-volume based numerical solver with a moving grid technique.
Abstract: The inertia plays a significant role in the response of a system undergoing flow-induced vibrations, which has been extensively investigated by previous researchers. However, the inertial effects of an energy harvester employing the mechanism of flow-induced vibrations have attracted little attention. This paper concentrates on a semi-passive energy extraction system considering its inertial effects. The incompressible Navier-Stokes equations are solved using a finite-volume based numerical solver with a moving grid technique. A partitioned method is used to couple the fluid and structure motions with the sub-iteration technique and an Aitken relaxation, which guarantees a strong fluid-structure coupling. In addition, a fictitious mass is added to resolve the numerical instability aroused by low density ratios. First, at a fixed mass ratio of r = 1, we identify an optimal set of parameters, at which a maximum efficiency of η = 34% is achieved. Further studies with r ranging from 0.125 to 100 are performed...
TL;DR: In this article, a Tuned Liquid Dampers (TLD) is proposed to mitigate the vibratory response of slender buildings by increasing the size of the perforated screen.
TL;DR: In this paper, the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow is considered and an equation of motion valid at small shear Reynolds numbers is obtained for spheroidal particles with arbitrary aspect ratios.
Abstract: We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits." We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyze how the linear stability of the "log-rolling" orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general, both unsteady and nonlinear terms in the Navier-Stokes equations are important.
TL;DR: In this article, a multi-variate Anisotropic Gaus-Sian closure for particle trajectory crossing (PTC) is proposed and validated for particle segregation in turbulent flows, in the spirit of the closure for out-of-equilibrium gas dynamics.
Abstract: The accurate simulation of disperse two-phase flows, where a discrete partic- ulate condensed phase is transported by a carrier gas, is crucial for many applications; Eulerian approaches are well suited for high performance computations of such flows. However when the particles from the disperse phase have a significant inertia compared to the time scales of the flow, particle trajectory crossing (PTC) occurs i.e. the particle ve- locity distribution at a given location can become multi-valued. To properly account for such a phenomenon many Eulerian moment methods have been recently proposed in the literature. The resulting models hardly comply with a full set of desired criteria involving: 1- ability to reproduce the physics of PTC, at least for a given range of particle inertia, 2- well-posedness of the resulting set of PDEs on the chosen moments as well as guaran- teed realizability, 3- capability of the model to be associated with a high order realizable numerical scheme for the accurate resolution of particle segregation in turbulent flows. The purpose of the present contribution is to introduce a multi-variate Anisotropic Gaus- sian closure for such particulate flows, in the spirit of the closure that has been suggested for out-of-equilibrium gas dynamics and which satisfies the three criteria. The novelty of the contribution is three-fold. First we derive the related moment systems of conservation laws with source terms, and justify the use of such a model in the context of high Knudsen numbers, where collision operators play no role. We exhibit the main features and advan- tages in terms of mathematical structure and realizability. Then a second order accurate and realizable MUSCL/HLL scheme is proposed and validated. Finally the behavior of the method for the description of PTC is thoroughly investigated and its ability to account accurately for inertial particulate flow dynamics in typical configurations is assessed.
TL;DR: In this article, the authors established the commonality of all extended magnetohydrodynamics (MHD) models through the use of suitable variable transformations, and they traced the existence of two Lie-dragged 2-forms, which are closely associated with the canonical momenta of the two underlying species.
Abstract: Through the use of suitable variable transformations, the commonality of all extended magnetohydrodynamics (MHD) models is established. Remarkable correspondences between the Poisson brackets of inertialess Hall MHD and inertial MHD (which has electron inertia, but not the Hall drift) and extended MHD (which has both effects) are established. The helicities (two in all) for each of these models are obtained through these correspondences. The commonality of all the extended MHD models is traced to the existence of two Lie-dragged 2-forms, which are closely associated with the canonical momenta of the two underlying species. The Lie-dragging of these 2-forms by suitable velocities also leads to the correct equations of motion. The Hall MHD Poisson bracket is analyzed in detail, the Jacobi identity is verified through a detailed proof, and this proof ensures the Jacobi identity for the Poisson brackets of all the models.
TL;DR: In this paper, a new methodology for online inertia parameters estimation for a rigid space debris captured by a tethered system, based on a new dynamics model of the system where the base satellite (chaser) and the space debris (target) are modeled as rigid bodies and the attachment points of the tether are offset from the centers of mass of the two bodies.
TL;DR: In this paper, it is shown that to each tetrad there is naturally a spin connection that locally removes the inertial effects from the action, and the use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values.
Abstract: In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.