Showing papers on "Equations of motion published in 1994"

Constant pressure molecular dynamics algorithms

Abstract: Modularly invariant equations of motion are derived that generate the isothermal–isobaric ensemble as their phase space averages. Isotropic volume fluctuations and fully flexible simulation cells as well as a hybrid scheme that naturally combines the two motions are considered. The resulting methods are tested on two problems, a particle in a one‐dimensional periodic potential and a spherical model of C60 in the solid/fluid phase.

Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid Part 1. Sedimentation

Abstract: This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

Flow-equations for Hamiltonians

Abstract: Flow-equations are introduced in order to bring Hamiltonians closer to diagonalization It is characteristic for these equations that matrix-elements between degenerate or almost degenerate states do not decay or decay very slowly In order to understand different types of physical systems in this framework it is probably necessary to classify various types of these degeneracies and to investigate the corresponding physical behavior In general these equations generate many-particle interactions However, for an n-orbital model the equations for the two-particle interaction are closed in the limit of large n Solutions of these equations for a one-dimensional model are considered There appear convergency problems, which are removed, if instead of diagonalization only a block-diagonalization into blocks with the same number of quasiparticles is performed

Geometric statistics in turbulence

Abstract: The author presents results regarding certain average properties of incompressible fluids derived from the equations of motion. The author estimates the average dissipation rate, the average dimension of level sets. The role played by the field of direction of vorticity in the three-dimensional Euler and Navier-Stokes equations is discussed and a class of two-dimensional equations that are useful models of incompressible dynamics is described. The author presents results concerning scaling exponents in turbulence.

Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures

Abstract: Part 1: general overview on the contents of the book. Part 2 Modelling of networks of elastic strings: modelling of nonlinear elastic strings networks of nonlinear elastic strings linearization wellposedness of the network equations controllability of networks of elastic strings - exact controllability of tree networks, lack of controllability for networks with closed circuits stabilizability of string networks string networks with masses at the nodes. Part 3 Networks of thermoelastic beams modelling of a thin thermoelastic curved beam the equations of motion - some remarks on warping and torsion rotating beams - dynamic stiffening nonlinear nonshearable 3-d beams - approximation-generalizations linear shearable 3-d beams nonlinear shearable 2-d beams - approximation-generalizations a list of beam models - damping networks of beams - geometric joint conditions, rigid joints pinned joints, dynamic joint conditions, rigid joints, pinned joints rotating two-link nonlinear shearable beams. Part 4 A general hyperbolic model for networks: the general model some special cases - string networks, networks of planar Timoshenko beams, networks of linear shearable beams, networks of initially curved bresse beams, beams and strings existence and regularity of solutions energy estimates for hyperbolic systems exact controllability of the network model stabilizability of the network model. Part 5 Spectral analysis and numerical simulation: eigenvalue problems for networks - notation networks of strings setworks of Timoshenko beams Euler-Bernoulli beams the eigenvalue problem for mechanical networks - the string case, homogeneous network of strings, examples, the homogenous Timoshenko network numerical simulations of controlled networks, introductory remarks, absorbing controls, cirecting controls finite element approximations of networks - dry friction at joints. Part 6 Interconnected membranes: modelling of dynamic nonlinear elastic membranes - equations of motion, edge conditions, Hamilton's Principle systems of interconnected elastic membranes - geometric junction conditions, dynamic conditions, linearization, well-posedness of the linear model controllability of linked isotropic membranes - observability estimates for the homogeneous problem, a priori estimates for serially connected membranes, a priori estimates for single jointed membrane systems, the reachable states, serially connected membranes, membrane transmission problems. Part 7 Systems of linked plates: modelling of dynamic nonlinear elastic plates (Part contents)

Averaged equations for inviscid disperse two-phase flow

Abstract: Averaged equations governing the motion of equal rigid spheres suspended in a potential flow are derived from the equation for the probability distribution. A distinctive feature of this work is the derivation of the disperse-phase momentum equation by averaging the particle equation of motion directly, rather than the microscopic equation for the particle material. This approach is more flexible than the usual one and leads to a simpler and more fundamental description of the particle phase. The model is closed in a systematic way (i.e. with no ad hoc assumptions) in the dilute limit and in the linear limit. One of the closure quantities is related to the difference between the gradient of the average pressure and the average pressure gradient, a well-known problem in the widely used two-fluid engineering models. The present result for this quantity leads to the introduction of a modified added mass coefficient (related to Wallis's ‘exertia’) that remains very nearly constant with changes in the volume fraction and densities of the phases. Statistics of this coefficient are provided and exhibit a rather strong variability of up to 20% among different numerical simulations. A detailed comparison of the present results with those of other investigators is given in § 10.As a further illustration of the flexibility of the techniques developed in the paper, in Appendix C they are applied to the calculation of the so-called ‘particle stress’ tensor. This derivation is considerably simpler than others available in the literature.

A dynamics-controlled truncation scheme for the hierarchy of density matrices in semiconductor optics

Abstract: We discuss the interaction of coherent electromagnetic fields with the semiconductor band edge in a dynamic density matrix model. Due to the influence of the Coulomb-interaction then-point density matrices are coupled in an infinite hierarchy of equations of motion. We show how this hierarchy is related to an expansion of the density matrices in terms of powers of the exciting field. We make use of the above results to set up a closed set of equations of motion involving two-, four-and six-point correlation functions, from which all third order contributions to the polarization can be calculated exactly. Comparison of our treatment of the hierarchy with the widely used RPA decoupling on the two-point level, gives interesting insight into the validity of the RPA. In particular we find, that a RPA-like factorization for two of the relevant density-matrices yields a solution of their respective equations of motion to lowest order in the electric field.

Equation of state and wave propagation in hysteretic nonlinear elastic materials

Abstract: Heterogeneous materials, such as rock, have extreme nonlinear elastic behavior (the coefficient characterizing cubic anharmonicity is orders of magnitude greater than that of homogeneous materials) and striking hysteretic behavior (the stress-strain equation of state has discrete memory). A model of these materials, taking their macroscopic elastic properties to result from many mesoscopic hysteretic elastic units, is developed. The Preisach-Mayergoyz description of hysteretic systems and effective medium theory are combined to find the quasistatic stress-strain equation of state, the quasistatic modulus-stress relationship, and the dynamic modulus-stress relationship. Hysteresis with discrete memory is inherent in all three relationships. The dynamic modulus-stress relationship is characterized and used as input to the equation of motion for nonlinear elastic wave propagation. This equation of motion is examined for one-dimensional propagation using a Green function method. The out-of-phase component of the dynamic modulus due to hysteresis is found to be responsible for the generation of odd harmonics and to determine the amplitude of the nonlinear attenuation.

Camrad - a comprehensive analytical model of rotorcraft aerodynamics and dynamics

Abstract: The Comprehensive Analytical Model of Rotorcraft Aerodynamics, CAMRAD, program is designed to calculate rotor performance, loads, and noise; helicopter vibration and gust response; flight dynamics and handling qualities; and system aeroelastic stability. The analysis is a consistent combination of structural, inertial, and aerodynamic models applicable to a wide range of problems and a wide class of vehicles. The CAMRAD analysis can be applied to articulated, hingeless, gimballed, and teetering rotors with an arbitrary number of blades. The rotor degrees of freedom included are blade/flap bending, rigid pitch and elastic torsion, and optionally gimbal or teeter motion. General two-rotor aircrafts can be modeled. Single main-rotor and tandem helicopter and sideby-side tilting proprotor aircraft configurations can be considered. The case of a rotor or helicopter in a wind tunnel can also be modeled. The aircraft degrees of freedom included are the six rigid body motion, elastic airframe motions, and the rotor/engine speed perturbations. CAMRAD calculates the load and motion of helicopters and airframes in two stages. First the trim solution is obtained; then the flutter, flight dynamics, and/or transient behavior can be calculated. The trim operating conditions considered include level flight, steady climb or descent, and steady turns. The analysis of the rotor includes nonlinear inertial and aerodynamic models, applicable to large blade angles and a high inflow ratio, The rotor aerodynamic model is based on two-dimensional steady airfoil characteristics with corrections for three-dimensional and unsteady flow effects, including a dynamic stall model. In the flutter analysis, the matrices are constructed that describe the linear differential equations of motion, and the equations are analyzed. In the flight dynamics analysis, the stability derivatives are calculated and the matrices are constructed that describe the linear differential equations of motion. These equations are analyzed. In the transient analysis, the rigid body equations of motion are numerically integrated, for a prescribed transient gust or control input. The CAMRAD program product is available by license for a period of ten years to domestic U.S. licensees. The licensed program product includes the CAMRAD source code, command procedures, sample applications, and one set of supporting documentation. Copies of the documentation may be purchased separately at the price indicated below. CAMRAD is written in FORTRAN 77 for the DEC VAX under VMS 4.6 with a recommended core memory of 4.04 megabytes. The DISSPLA package is necessary for graphical output. CAMRAD was developed in 1980.

System for encoding image data into multiple layers representing regions of coherent motion and associated motion parameters

Abstract: A system stores images as a series of layers by determining (i) the boundaries of regions of coherent motion over the entire image, or frame, sequence; and (ii) associated motion parameters, or coefficients of motion equations, that describe the transformations of the regions from frame to frame. The system first estimates motion locally, by determining the movements within small neighborhoods of pixels from one image frame i to the next image frame i+1, to develop an optical flow, or dense motion, model of the image. Next, the system estimates the motion using affine or other low order, smooth transformations within a set of regions which the system has previously identified as having coherent motion, i.e., identified by analyzing the motions in the frames i-1 and i. It groups, or clusters, similar motion models and iteratively produces an updated set of models for the image. The system then uses the local motion estimates to associate individual pixels in the image with the motion model that most closely resembles the pixel's movement, to update the regions of coherent motion. Using these updated regions, the system iteratively updates its motion models and, as appropriate, further updates the coherent motion regions, and so forth. The system then does the same analysis for the remaining frames. The system next segments the image into regions of coherent motion and defines associated layers in terms of (i) pixel intensity values, (ii) associated motion model parameters, and (iii) order in "depth" within the image.

Modification of the Euler equations for ``vorticity confinement'': Application to the computation of interacting vortex rings

Abstract: A new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admit solutions that consist of Lagrangian‐like confined vortical regions, or covons, in the shape of two‐dimensional (2‐D) vortex ‘‘blobs’’ and three‐dimensional (3‐D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. The discretized Euler equations with the extra term ca...

Dynamic soil pressures on rigid vertical walls

Abstract: A critical evaluation is made of the dynamic pressures and the associated forces induced by ground shaking on a rigid, straight, vertical wall retaining a semi-infinite, uniform viscoelastic layer of constant thickness. The effects of both harmonic and earthquake-induced excitations are examined. Simple approximate expressions for the responses of the system are developed, and comprehensive numerical data are presented which elucidate the effects and relative importance of the various parameters involved. These solutions are then compared with those obtained by use of a simple model proposed previously by Scott, and the accuracy of this model is assessed. Finally, two versions of an alternative model are proposed which better approximate the action of the system. In the first, the properties of the model are defined by frequency-dependent parameters, whereas in the second, which is particularly helpful in analyses of transient response, they are represented by frequency-independent, constant parameters.

Wave- and Wind-Driven Flow in Water of Finite Depth

Abstract: The authors first derive both Coriolis-induced and viscosity-induced stresses for arbitrary water depth and arbitrary wave direction. Opportunity is taken here to succinctly and rigorously derive the Longuet-Higgins virtual tangential stress due to wave motion. It is shown that the virtual stress is a projection on the surface slope of two viscous normal stresses acting on the vertical and horizontal planes. Then a simple Eulerian model is presented for the steady flow driven by waves and by waves and winds This simple Eulerian model demonstrates that the wave forcing can he easily incorporated with other conventional forcing, rather than resorting to a complicated and lengthy perturbation analysis of the Lagrangian equations of motion. A further focus is given to the wave-driven flow when the various limits of the wave-driven steady flow are discussed. The wave-driven steady flow given by the model yields a unified formula between Ursell and Hasselmann's inviscid but rotational theory and the Lo...

Energy-momentum conservation in gravity theories.

Abstract: We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail. In 2+1 dimensions, expressions are obtained for energy and angular momentum arising in the ISO(2,1) gauge-theoretical formulation of Einstein gravity. In addition, an expression for energy in a gauge-theoretical formulation of the string-inspired (1+1)-dimensional gravity is derived and compared with the ADM definition of energy.

A characteristic-based method for incompressible flows

Abstract: A new characteristic-based method for the solution of the 2D laminar incompressible Navier-Stokes equations is presented. For coupling the continuity and momentum equations, the artificial compressibility formulation is employed. The primitives variables (pressure and velocity components) are defined as functions of their values on the characteristics. The primitives variables on the characteristics are calculated by an upwind diffencing scheme based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. The upwind scheme uses interpolation formulae of third-order accuracy. The time discretization is obtained by the explicit Runge–Kutta method. Validation of the characteristic-based method is performed on two different cases: the flow in a simple cascade and the flow over a backwardfacing step.

Effective Lagrangians with higher derivatives and equations of motion

Abstract: The problems that are connected with Lagrangians which depend on higher derivatives (namely, additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of motion may be used to eliminate all higher time derivatives from the effective interaction term. The application of the equations of motion can be realized by making field transformations that involve derivatives of the fields. Using the Hamiltonian formalism for higher-order Lagrangians (Ostrogradsky formalism), Lagrangians that are related by such transformations are shown to be physically equivalent (at the classical and at the quantum level). The equivalence of Hamiltonian and Lagrangian path integral quantization (Matthews's theorem) is proven for effective higher-order Lagrangians. Effective interactions of massive vector fields involving higher derivatives are examined within gauge noninvariant models as well as within (linearly or non-linearly realized) spontaneously broken gauge theories. The Stueckelberg formalism, which relates gauge noninvariant to gauge invariant Lagrangians, becomes reformulated within the Ostrogradsky formalism.

Parameter identification of unknown object handled by free-flying space robot

Abstract: This paper is concerned with parameter identification methods for inertial parameters of the unknown object handled by manipulators on a free-flying space robot. The parameter identification is necessary for precise control because the payload changes the kinematics of the system together with the dynamics. Two methods are proposed under the condition that the robot is free to translate and rotate. One method is based on the conservation principle of linear and angular momentum and the other on Newton-Euler equations of motion. Only the linear/ angular velocities and accelerations of the satellite base are used in the identification methods with no information about the force and torque utilized. The feasibility of the methods is demonstrated by a hardware experiment on the ground as well as numerical simulation.

Power-Law Fluid-Flow over Spheroidal Particles

Abstract: The equations of motion have been solved numerically for the incompressible power law fluid flow past spherical and spheroidal solid particles. The finite element technique has been employed to obtain the velocity and pressure fields prevailing around a particle. These have been further processed to evaluate the individual contributions of pressure and viscous forces to the total drag on spheres and spheroids (prolates and oblates). Streamline plots showing the nature of flow and the gradual development of the wake region are also presented. The computed drag results encompass wide ranges of physical and kinematic conditions given by 1≥n≥0.4, 0.01≤Re≤100, and 0.2≤E≤5.

Rotational response and slip prediction of serpentine belt drive systems

Abstract: A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single {long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closedform procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.

Transverse particle motion in radio-frequency linear accelerators

Abstract: The transverse motion of a relativistic charged particle in a radio-frequency linear accelerator (rf linac) is examined. The spatially averaged equations of motion are derived for a particle in a periodic accelerating cavity system, and solved exactly in the ultrarelativistic limit. These solutions, along with an impulse treatment of the transients at the entrance and exit of the linac cavities, allow derivation of a linear transport matrix through the cavity. This generalized matrix is improved over previously derived results in that it is applicable to both traveling- and standing-wave structures, allows for arbitrary injection phase and spatial-harmonic content of the rf fields, and is more accurate in approximating the exact charged-particle motion.