Euler Equations Of Motion Research Articles

Investigation of the position error signal of an operating hard disk drive due to varying temperature conditions

Electromechanical analysis was employed to investigate how variations of hard disk drive (HDD) temperature affect the position error signal of the read/write head. Electromagnetic fields of the spindle motor and voice coil motor were analyzed by solving time-stepping finite element equations. The motional analysis of the rotating spindle and actuator was performed using the Newton–Euler equation of motion. The control actions of the disk speed and track following motion of actuator are included for the numerical description of the data access. The simulation results showed how the operating temperature dependence of HDD variables such as the coil resistances, magnetization of the permanent magnet, fluid viscosity in the fluid dynamic bearing and thermal expansion of the structures, affect the electromechanical characteristics of the HDD system. Also, the results showed that the increased position error signal of the head at an elevated operating temperature was mainly caused by increased disk run-out. The latter phenomenon was due to a degradation of performance in the fluid dynamic bearing in the rotating disk-spindle system. These results were verified by experimental testing.

Energy-Vorticity Theory of Ideal Fluid Mechanics

Nambu field theory, originated by Névir and Blender for incompressible flows, is generalized to establish a unified energy–vorticity theory of ideal fluid mechanics. Using this approach, the degeneracy of the corresponding noncanonical Poisson bracket—a characteristic property of Hamiltonian fluid mechanics—can be replaced by a nondegenerate bracket. An energy–vorticity representation of the quasigeostrophic theory and of multilayer shallow-water models is given, highlighting the fact that potential enstrophy is just as important as energy. The energy–vorticity representation of the hydrostatic adiabatic system on isentropic surfaces can be written in complete analogy to the shallow-water equations using vorticity, divergence, and pseudodensity as prognostic variables. Furthermore, it is shown that the Eulerian equation of motion, the continuity equation, and the first law of thermodynamics, which describe the nonlinear evolution of a 3D compressible, adiabatic, and nonhydrostatic fluid, can be written in Nambu representation. Here, trilinear energy–helicity, energy–mass, and energy–entropy brackets are introduced. In this model the global conservation of Ertel’s potential enstrophy can be interpreted as a super-Casimir functional in phase space. In conclusion, it is argued that on the basis of the energy–vorticity theory of ideal fluid mechanics, new numerical schemes can be constructed, which might be of importance for modeling coherent structures in long-term integrations and climate simulations.

A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints

A Riemannian-geometry approach for modeling and control of dynamics of object manipulation under holonomic or non-holonomic constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a holonomic constraint is reinterpreted in terms of “submersion” in Riemannian geometry. A force control signal constructed in the image space of the constraint gradient is regarded as a lifting (or pressing) in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability of position control under holonomic constraints is discussed. Second, modeling and control of two-dimensional object grasping by a pair of multijoint robot fingers are challenged, when the object is of arbitrary shape. It is shown that rolling contact constraints induce the Euler equation of motion, in which constraint forces appear as wrench vectors affecting the object. The Riemannian metric is introduced on a constraint submanifold characterized with arclength parameters. An explicit form of the quotient dynamics is expressed in the kernel space with accompaniment of a pair of first-order differential equations concerning the arclength parameters. An extension of Dirichlet-Lagrange's stability theorem to redundant systems under constraints is suggested by introducing a Morse-Lyapunov function.

Cluster computing of mechanisms dynamics using recursive formulation

This paper presents the O(n) recursive algorithm for forward dynamics of closed loop kinematic chains adapted to parallel computations on a cluster of workstations. The Newton–Euler equations of motion are formulated in terms of relative coordinates. Closed loop kinematic chains are transformed into open loop chains by cut joint technique. Cut joint constraint and Lagrange multipliers are introduced to complete the equations of motion. Constraint stabilization is performed using the Baumgarte stabilization technique with application to multibody systems with large number of degrees of freedom. Numerical simulations are carried out to study the influence of the degrees of freedom of the multibody system on computational efficiency of the algorithm using the Message Passing Interface (MPI). We also consider the ways of minimization of communication overhead which has significant impact on efficiency in case of cluster computing.

The Hamiltonian formalism and a new type of modulation instability

We recently reported the existence of a new type of modulation instability of the waves on the surface of ideal fluid (2006 J. Phys. A: Math. Gen. 39 L529). To this end, we considered the system of two equations of motion for the amplitude of the envelope of the first harmonic and for the nonoscillating wave component (zero harmonic) in the framework of the method of multiple scales and the Euler equations of motion. Here, this new type of modulation instability is reproduced with the use of the Zakharov equations for the Fourier amplitudes of the first and zero harmonics on the basis of the Hamiltonian formalism.

Numerical modelling of a high-speed rigid rotor in a single-aerostatic bearing using modified Euler equations of motion

Accurate rotordynamic analysis is critical in the achievement of efficient rotary machine design, however the majority of models concern flexible shafts with concentrated supports. The modified Euler equations of motion are used in a numerical model to calculate the natural frequencies and whirl amplitudes of a rigid rotor supported by a single-aerostatic bearing. The bearing is modelled with a non-constant stiffness distribution along its length and a non-symmetric centre of gravity. The results are compared with experimental modal analysis (EMA).

Simulated Doppler Velocity Signatures of Evolving Tornado-Like Vortices

Abstract Exact solutions of the Navier–Stokes or Euler equations of motion and the continuity equation in cylindrical coordinates for 3D, axisymmetric, inviscid, or laminar flows are utilized to represent evolving vortices that roughly model tornado cyclones or misocyclones contracting to tornadoes. These solutions are unsteady versions of the diffusive Burgers–Rott vortex and the inviscid Rankine-combined vortex. They satisfy the free-slip condition at the ground. Different vortices are obtained by choosing different values of the constant eddy viscosity and uniform horizontal convergence while holding the circulation at infinity constant. A simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) is employed to generate time-varying Doppler velocity signatures in uniform reflectivity of these analytical vortices at ranges of 25 and 50 km from the radar. Mean Doppler velocities are determined by computing 3D integrals over effective resolution volumes. Magnitudes of Doppler vortex signatures at different times in the evolution of the stationary vortices are computed for effective beamwidths of 1.02° and 1.39°, which correspond to azimuthal sampling intervals of 0.5° and 1.0°, respectively. Four tornado predictors—rotational velocity, shear, excess rotational kinetic energy, and circulation—are examined. Results of the simulations show that for smaller effective beamwidths, Doppler vortex signatures are stronger and exceed fixed threshold values of rotational velocity and shear earlier. With finer azimuthal resolution, tornado cyclone, misocyclone, or tornado signatures switch to tornadic vortex signatures later. Circulations of the vortex signatures give good estimates of the circulations of the simulated tornadoes and tornado cyclones with relative insensitivity to range, effective beamwidth, and stage of evolution. High circulation and convergence values of a rotation signature reveal the potential for a tornado earlier than all the other predictors, which increase significantly during tornadogenesis.

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

Geometrical Aspects in Hydrodynamics and Integrable Systems

The motion of fluid particles of an inviscid incompressible fluid on a bounded domain is formulated from a Lagrangian point of view. This is accomplished by observing that Euler's equation of motion is a geodesic equation on a group of volume-preserving diffeomorphisms with the metric defined by the kinetic energy. This formulation is based on Riemannian geometry and Lie group theory, first developed by Arnold (1966). Behaviors of the geodesics are characterized by Riemannian (sectional) curvatures, which are shown to be mostly negative (with some exceptions). This property is related to the mixing and ergodicity of the fluid motions. Free rotation of a rigid body fixed at a point gives a simplest example of the dynamical systems which are integrable and represented with such formulation. The same method is applied to the other integrable systems such as the vortex-filament equation or the KdV equation. In contrast to the hydrodynamic system, sectional curvatures are found to be mostly positive (with exceptions). Thus it is found that integrable systems are more stable in the behavior of geodesics than the hydrodynamic system governed by the Euler's equation of motion.

The Effect of Fiber Inertia on Its Orientation in a Shear Flow with Application to Lung Dosimetry

The effect of fiber inertia on its orientation in a flow field was studied. Expressions for fluid dynamic torque given by Jeffery (1923) were used in the Euler equations of motion to determine fiber orientation. Fiber orientation was found to depend on two nondimensional parameters; its aspect ratio and a nondimensional parameter related to the fluid viscosity, flow velocity gradient, and fiber mass density and diameter. Fiber orientation was calculated for different fiber diameters and was compared with that obtained by Jeffery (1923) for normal breathing in humans and rats. The inertial effects are significant when fiber diameter exceeds lμm.

Numerical study of two-fluid C-type shock waves

view Abstract Citations (31) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Numerical Study of Two-Fluid C-Type Shock Waves Toth, Gabor Abstract C-type magnetohydrodynamic shocks in the partially ionized interstellar medium are studied in the two-fluid approximation. The ionized fluid can move along the magnetic field lines, while it interacts with the neutral fluid via ion-neutral elastic scattering. I use an explicitly flux-conserving two-dimensional Eulerian flux-corrected transport code to study the dynamics of two-fluid shocks. A numerical instability intrinsic to two-fluid problems was discovered, and a solution to the problem is proposed. The code can successfully simulate C-type shocks. The results of the linear stability analysis by Wardle are confirmed, and the nonlinear behavior of the instability is explored. Publication: The Astrophysical Journal Pub Date: April 1994 DOI: 10.1086/173973 Bibcode: 1994ApJ...425..171T Keywords: Computational Astrophysics; Elastic Scattering; Euler Equations Of Motion; Interstellar Matter; Magnetohydrodynamics; Numerical Analysis; Shock Waves; Two Dimensional Models; Two Fluid Models; Algorithms; Boundary Conditions; Computerized Simulation; Differential Equations; Grid Generation (Mathematics); Linear Equations; Nonlinearity; Astrophysics; METHODS: NUMERICAL; MAGNETOHYDRODYNAMICS: MHD; SHOCK WAVES full text sources ADS |

Kinetic flux vector splitting for euler equations

This paper is mainly concerned with the development of a class of new upwind methods and a novel treatment of the boundary condition based on the concept of kinetic flux vector splitting (KFVS) for solving inviscid gasdynamic problems. KFVS utilizes the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a Maxwellian. After presentation of the analysis of the KFVS method in I-D in detail, it is described how KFVS can be performed in a different manner to construct various upwind methods for higher dimensions depending on the situations. Next, it is shown how the KFVS formulation together with the specular reflection model of the kinetic theory of gases at the solid boundary lead to the development of a new treatment of the flow tangency boundary condition which is robust, upwind and conservative and does not require any further assumptions or the use of fictitious grid points. Finally, the present method is tested on a wide variety of problems to demonstrate its capability in obtaining accurate and wiggle-free solutions.

The Euler Equations of Motion with Hydrostatic Pressure as an Independent Variable

Abstract A novel form of the Euler equations is developed through the use of a different vertical coordinate system. It is shown that the use of hydrostatic pressure as an independent variable has the advantage that the Euler equations then take a form that parallels very closely the form of the hydrostatic equations cast in isobaric coordinates. This similarity holds even when topography is incorporated through a further transformation into terrain-following coordinates. This leads us to suggest that hydrostatic-pressure coordinates could be used advantageously in nonhydrostatic atmospheric models based on the fully compressible equations.

Nonlinear superposition of solutions to self-gravitating fluid equations

view Abstract Citations (1) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonlinear Superposition of Solutions to Self-gravitating Fluid Equations Amendt, Peter ; Lanza, Antonio Abstract An analytic procedure for nonlinearly superposing axisymmetric, stationary, self-gravitating solutions to Euler's equation or the Jeans equations to generate new and more general classes of solutions is presented. Two examples of the method are given. The first uses a nonlinear superposition of two Maclaurin spheroids to produce a large family of self-gravitating toroidal solutions of Euler's equation. The second example examines some possible consequences of the nonlinear superposition on galactic mass modeling studies based on the Jeans equations. It is shown that (1) regions of reduced stellar density may lead to local angular momentum enhancement and (2) a flat composite rotation velocity profile may be nonlinearly constructed from two or more mass components with decreasing rotation curves. Publication: The Astrophysical Journal Pub Date: February 1990 DOI: 10.1086/168414 Bibcode: 1990ApJ...350..597A Keywords: Euler Equations Of Motion; Fluid Dynamics; Galactic Rotation; Gravitation; Superposition (Mathematics); Angular Momentum; Poisson Equation; Star Distribution; Astrophysics; GALAXIES: INTERNAL MOTIONS; HYDRODYNAMICS; ROTATION full text sources ADS |

Three-Dimensional Sloshing of Water on Decks

A methodology is proposed to solve the problem of the three-dimensional flow of water sloshing on the deck of a vessel, and to calculate the resulting forces and moments at the center of gravity. The Eulerian equations of motion of the water particle for incompressible inviscid shallow water flow are formulated with respect to a system attached to the oscillating vessel. The system of the nonlinear hyperbolic equations of motion is solved numerically using Glimm's method (random-choice method). Complex flow patterns consisting of oblique bores and "swirling" motions of the water on deck were revealed, for a vessel oscillating in roll and pitch motions, for a wide range of excitation frequencies. Large accumulation of water occurs at the corners while parts of the deck become dry. Significant rolling moments due to sloshing are exerted on the vessel. These must be taken into account when the dynamic response of the vessel is studied.

A many-body Lagrangian for celestial body dynamics to second post-Newtonian linear field order

view Abstract Citations (9) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Many-Body Lagrangian for Celestial Body Dynamics to Second Post-Newtonian Linear Field Order Benacquista, M. ; Nordtvedt, K. Abstract The many-body Lagrangian formalism developed by Nordvedt is used to develop an extension of the first post-Newtonian Lagrangian for compact celestial bodies interacting via an underlying metric theory of gravity. The Lagrangian is extended to second order in the motion of the bodies but is linear in the potentials. A hierarchy of Lorentz invariances is then imposed on this "linear field" Lagrangian, and the resulting Lorentz-invariant Lagrangian is found to depend solely on the structure of the first post-Newtonian Lagrangian. Publication: The Astrophysical Journal Pub Date: May 1988 DOI: 10.1086/166316 Bibcode: 1988ApJ...328..588B Keywords: Celestial Bodies; Euler Equations Of Motion; Gravitation Theory; Lorentz Force; Many Body Problem; Computational Astrophysics; Degrees Of Freedom; Astrophysics; GRAVITATION; RELATIVITY full text sources ADS |

THERMAL DEFORMATIONS AND STRESSES IN CIRCULARLY CURVED THIN BEAMS AND RINGS

A consistent treatment of the combined effects of extensional, flexural, and shearing deformations of thin, circularly curved beams and rings subjected to thermal loads of arbitrary variation, and general distributed and concentrated in-plane loads is presented. The present treatment, which deals with the problem in its general form, has been developed from variational considerations using Hamilton's principle to derive the exact Euler equations of motion and consistent boundary conditions for thin rings and curved beams in terms of the radial and tangential midsurface displacements and the rotation of the normal that, concomitantly, include the effects of extensional and shearing deformations. Discontinuity conditions corresponding to discrete application of generalized forces and consistent conditions on the time axis are also obtained. For static analysis, the coupled Euler equations of motion are transformed into three uncoupled differential equations, sixth-order in radial and tangential displacement...

Local interstellar gasdynamical stability and substructure in spiral arms

view Abstract Citations (78) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local Interstellar Gasdynamical Stability and Substructure in Spiral Arms Balbus, Steven A. Abstract A rather general local dynamical stability analysis for interstellar gas flow through the spiral arm regions (or regions with similar oblique potentials) in disk galaxies is presented. The background flow may in principal be quite arbitrary as long as the gas orbits remain approximately circular; highly compressed flow is permitted. A polytropic single-fluid treatment is used. All perturbation wavenumbers in the plane of the disk are considered. The calculations reduce to the Goldreich-Lynden-Bell (GLB) swing amplifier in the limit of unit enhancement (i.e., no compression) in the spiral arm. Our results thus generalize both GLB and an earlier paper by Balbus and Cowie (BC) in which Jeans-like disturbances were analyzed. If the underlying galactic rotation curve is flat, then density compressions greater than a factor of 2 cause the background angular velocity locally to increase outward. This disrupts the classical swing amplification mechanism by destroying the consonance of the epicyclic and shear motion. This would tend to cause unsheared tightly wound disturbances to grow most rapidly. But opposing this tendency is a divergence swing amplifier: the underlying expansion of the flow, being nonisotropic in the disk plane, generally both separates and rotates wave crests in a perturbation. (Similar effects are associated with compression). If this induced rotation is in the same sense as the epicyclic motion, then amplification can occur. This process favors loosely wound, unwrapped perturbations. Growth rates for both the tightly and loosely wound arms can be comparable and depend upon the overall stability of the underlying flow: more sensitive flow favors tightly wrapped disturbances; less sensitive (but still responsive) flow favors loosely-wrapped wavelets. Because expanding flow tends to resist winding, the latter may be associated with periodic spurs often seen protruding from principal arms in spiral galaxies, particularly in the outer regions of the disk. Another possible generating mechanism for spurs or branches is that tightly-wound growing wave crests can be distorted by the tidal velocity field which is both expanding and changing shear direction near the arm. This depends upon departures from uniform expansion and is accordingly a higher order effect that can be treated via local analysis. These structures need not be periodically spaced along an arm. When the most rapidly growing tight and loose wavelets respond on a comparable time scale, nonlinear periodic structure may be expected to appear at the intersections of wave crests. We identify these with cloud complexes. Characteristic spacings and masses are in agreement with observations. A morphological progression-thickened arms with irregular structure, arms with periodic structure, highly branched or spurred arms-is suggested by the results, with the BC local stability parameter Q_sp_ (or its equivalent) determining the outcome. Publication: The Astrophysical Journal Pub Date: January 1988 DOI: 10.1086/165880 Bibcode: 1988ApJ...324...60B Keywords: Disk Galaxies; Dynamic Stability; Galactic Structure; Gas Dynamics; Interstellar Gas; Spiral Galaxies; Density Distribution; Euler Equations Of Motion; Perturbation Theory; Astrophysics; GALAXIES: STRUCTURE; HYDRODYNAMICS; INSTABILITIES full text sources ADS | data products SIMBAD (1) NED (1)

A general Eulerian formulation of the comoving-frame equation of radiative transfer

view Abstract Citations (24) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A General Eulerian Formulation of the Comoving-Frame Equation of Radiative Transfer Riffert, H. Abstract For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. Publication: The Astrophysical Journal Pub Date: November 1986 DOI: 10.1086/164726 Bibcode: 1986ApJ...310..729R Keywords: Computational Astrophysics; Euler Equations Of Motion; Hydrodynamic Equations; Radiative Transfer; Fluid Flow; Schwarzschild Metric; Astrophysics; HYDRODYNAMICS; RADIATIVE TRANSFER full text sources ADS |

Evolution of twisted magnetic fields

view Abstract Citations (48) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Evolution of twisted magnetic fields Zweibel, E. G. ; Boozer, A. H. Abstract The magnetic field of the solar corona evolves quasi-statically in response to slowly changing photospheric boundary conditions. The magnetic topology is preserved by the low resistivity of the solar atmosphere. It is shown that a magnetic flux coordinate system simplifies the problem of calculating field evolution with invariant topology. As an example, the equilibrium of a thin magnetic flux tube with small twist per unit length is calculated. Publication: The Astrophysical Journal Pub Date: August 1985 DOI: 10.1086/163407 Bibcode: 1985ApJ...295..642Z Keywords: Magnetic Field Configurations; Magnetic Flux; Magnetohydrodynamic Stability; Photosphere; Solar Corona; Solar Magnetic Field; Cartesian Coordinates; Differential Equations; Euler Equations Of Motion; Integral Equations; Topology; Solar Physics full text sources ADS |