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Showing papers on "Equations of motion published in 1991"


Journal ArticleDOI
TL;DR: In this paper, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) are re-examined in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed.
Abstract: This paper is mainly concerned with a re-examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics. However, the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed. More specifically, after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) is re-examined. This includes some differences from the usual procedure on the subject. Next, thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables, a discussion of a theory of heat (or a purely thermal theory) is provided which differs from the usual development in the classical thermodynamics. A detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well-motivated constitutive equations. Special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves. The remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject.

1,065 citations


Journal ArticleDOI
TL;DR: In this paper, the qualitative properties of an inviscid, incompressible, two-dimensional fluid are examined starting from the equations of motion, and a series of equations govern the behavior of the spatial gradients of the vorticity scalar.

955 citations


Journal ArticleDOI
TL;DR: Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures in this paper, where the mechanical properties of damping materials are modeled using fractional order time derivatives of stress and strain.
Abstract: Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures. The mechanical properties of damping materials are modeled using fractional order time derivatives of stress and strain. These models accurately describe the broadband effects of material damping in the structure's equations of motion. The resulting structural equations of motion are used to derive the fractional order state equations. Substantial differences between the structural and state equations are seen to exist. The mathematical form of the state equations suggests the feedback of fractional order time derivatives of structural displacements to improve control system performance. Several other advantages of the fractional order state formulation are discussed. Nomenclature

680 citations


Journal ArticleDOI
TL;DR: In this article, a model to predict the flow of an initially stationary mass of cohesionless granular material down rough curved beds is described, where the constitutive behaviour of the material making up the pile is described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption.
Abstract: This paper describes a model to predict the flow of an initially stationary mass of cohesion-less granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depthh and the depth averaged velocityū. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche lengthL, a characteristic heightH, and a characteristic bed radius of curvatureR. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio e-H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle δ and the characteristic non-dimensional curvature λ=L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order e for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.

482 citations


Book
01 Jan 1991
TL;DR: In this article, the authors propose a special theory of relativity for the weak gravitational field and a theory of the singularity of the Earth's magnetic field. But the theory is restricted to a single body problem and is not applicable to other bodies.
Abstract: MATHEMATICAL TOOLS Elements of Newtonian celestial mechanics Elements of Riemannian geometry and tensor analysis Elements of special theory of relativity GRT FIELD EQUATIONS Basic principles of GRT Weak gravitational field Problem of measurable quantities in GRT ONE-BODY PROBLEM Schwarzschild problem Light propagation in the Schwarzschild problem Field of rotating spheroid APPROXIMATE SOLUTIONS OF THE FIELD EQUATIONS AND APPROXIMATE EQUATIONS OF MOTION N-body problem Geocentric reference frame Equations in variations for the spherically symmetrical metric spaces Gravitational radiation and motion in binary system EQUATIONS OF MOTION OF SOLAR SYSTEM BODIES Equations of motion of Earth's artificial satellites Motion of the major planets Motion of the Moon RELATIVISTIC REDUCTION OF ASTROMETRIC MEASUREMENTS General principles of reduction Relativistic theory of astronomical reference systems Relativistic reduction of astrometric observations Relativistic reduction of radio observations RELATIVISTIC EFFECTS IN GEODYNAMICS Timescales on Earth Clocks and satellites in the circumterrestrial space Postcript References Index

420 citations


Journal ArticleDOI
01 Jul 1991
TL;DR: Closed-form equations of motion are presented for planar lightweight robot arms with multiple flexible links based on standard frame transformation matrices describing both rigid rotation and flexible displacement, under small deflection assumption.
Abstract: Closed-form equations of motion are presented for planar lightweight robot arms with multiple flexible links. The kinematic model is based on standard frame transformation matrices describing both rigid rotation and flexible displacement, under small deflection assumption. The Lagrangian approach is used to derive the dynamic model of the structure. Links are modeled as Euler-Bernoulli beams with proper clamped-mass boundary conditions. The assumed modes method is adopted in order to obtain a finite-dimensional model. Explicit equations of motion are detailed for two-link case assuming two modes of vibration for each link. The associated eigenvalue problem is discussed in relation with the problem of time-varying mass boundary conditions for the first link. The model is cast in a compact form that is linear with respect to a suitable set of constant parameters. Extensive simulation results that validate the theoretical derivation are included. >

372 citations


Journal ArticleDOI
TL;DR: A new formalism for treating the general-relativistic celestial mechanics of systems of system of arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies is presented, aimed at yielding a complete description of the global dynamics of such $N-body systems.
Abstract: We present a new formalism for treating the general-relativistic celestial mechanics of systems of $N$ arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such $N$-body systems ("external problem"), (ii) the local gravitational structure of each body ("internal problem"), and, (iii) the way the external and the internal problems fit together ("theory of reference systems"). This formalism uses in a complementary manner $N+1$ coordinate charts (or "reference systems"): one "global" chart for describing the overall dynamics of the $N$ bodies, and $N$ "local" charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these $N+1$ reference systems is a systematic use of a particular "exponential" parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue. Our scheme differs from previous attempts in several other respects: the structure of the stress-energy tensor is left completely open; the spatial coordinate grid (in each system) is fixed by algebraic conditions while a convenient "gauge" flexibility is left open in the time coordinate [at the order $\ensuremath{\delta}t=O({c}^{\ensuremath{-}4})$]; the gravitational field locally generated by each body is skeletonized by particular relativistic multipole moments recently introduced by Blanchet and Damour, while the external gravitational field experienced by each body is expanded in terms of a particular new set of relativistic tidal moments. In this first paper we lay the foundations of our formalism, with special emphasis on the definition and properties of the $N$ local reference systems, and on the general structure and transformation properties of the gravitational field. As an illustration of our approach we treat in detail the simple case where each body can, in some approximation, be considered as generating a spherically symmetric gravitational field. This "monopole truncation" leads us to a new (and, in our opinion, improved) derivation of the Lorentz-Droste-Einstein-Infeld-Hoffmann equations of motion. The detailed treatment of the relativistic motion of bodies endowed with arbitrary multipole structure will be the subject of subsequent publications.

284 citations


Journal ArticleDOI
TL;DR: In this paper, the authors analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe and show that the exchange of momentum in collisions between the grains and between the grain and the wall plays a significant role in the balance of forces in the particle phase.
Abstract: We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

212 citations


Book
01 Jun 1991
TL;DR: In this article, D'Alember's Principle and Lagrange Equations of Motion are combined with the concept of virtual work, and the first integral integral of the Equation of Motion is presented.
Abstract: 1. Kinematics.- 2. Statics, Systems of Forces, Hydrostatics.- 3. Mechanical Work, Power, Potential Energy.- 4. Constitutive Equations.- 5. Principle of Virtual Work.- 6. Selected Topics of Elastostatics.- 7. Dynamics of Solids and Fluids, Conservation of Momentum of Material and Control Volumes.- 8 First Integrals of the Equations of Motion, Kinetic Energy.- 9. Stability Problems.- 10. D'Alember's Principle and Lagrange Equations of Motion.- 11. Some Approximation Methods of Dynamics and Statics.- 12. Impact.- 13. Elementary Supplements of Fluid Dynamics.- 14. Selected Problems.- Table A. Some Average Values of Mechanical Material Parameters.- Table B. U.S. (Basic) Customary Units and Their SI Equivalents.

209 citations



Journal ArticleDOI
TL;DR: In this article, a singular integral equation technique for solving dynamic poroelasticity problems is presented using total stress variables instead of the partial stress ones in Biot's formulation.
Abstract: This paper presents a singular integral equation technique for solving dynamic poroelasticity problems. The poroelastic governing equations are presented using total stress variables instead of the partial stress ones in Biot's formulation. It is then established that there exists an analogy between the dynamic thermoelasticity and the dynamic poroelasticity if they are formulated in the frequency domain. The integral equations are derived based on the reciprocity energy principle. The fundamental solutions of point force and source are obtained from thermoelasticity literature according to the analogy. A two‐dimensional boundary element program is developed for the numerical solution. To verify the computer code, several fundamental one‐dimensional problems involving poroelastic columns excited either from the top or at the bottom by stress, pressure, or displacement are examined using both the boundary element technique and the exact solutions. In two‐dimensional geometry, we investigate a soil stratum ...

Journal ArticleDOI
TL;DR: In this article, a general, two-dimensional formulation for the response of free-standing rigid bodies to base excitation is presented, which is described in terms of the five possible modes of response (rest, slide, rock, slide-rock, and free-flight) and impact between the body and foundation.
Abstract: This paper presents the general, two‐dimensional formulation for the response of free‐standing rigid bodies to base excitation. The formulation assumes rigid body, rigid foundation, and Coulomb friction. The behavior is described in terms of the five possible modes of response (rest, slide, rock, slide‐rock, and free‐flight) and impact between the body and foundation. The governing equations of motion are summarized for the modes: slide, rock, and slide‐rock. Approximate equations are outlined for the rock and slide‐rock modes that are valid for small angles of rotation. A model governing impact from a rock, slide‐rock or free‐flight mode is derived from first principles using classical impact theory. This model assumes a point‐impact, nonzero coefficient of restitution and finite value of friction. The paper presents a complete and consistent formulation, which can be used in its entirety or in part, for investigation of the generalized response using suitable analytical or numerical techniques.

Journal ArticleDOI
TL;DR: In this paper, the authors considered general coordinate invariant equations of motion of interacting gauge fields of all spins s = 0, 1/2, 1,..., infinity in 3+1 dimensions.
Abstract: Properties of totally consistent equations of motion of interacting gauge fields of all spins s=0, 1/2, 1, . . ., infinity in 3+1 dimensions are discussed in some detail. The equations under consideration are explicitly general coordinate invariant, possess all necessary higher-spin gauge symmetries, reduce to the standard free massless equations in the linearized approximation and contain Einstein equations with the cosmological term in the spin-2 sector.

Journal ArticleDOI
Leonard Meirovitch1
TL;DR: In this paper, the general motion of a flexible body in space is derived using the extended Hamilton's principle for distributed systems, and the standard Lagrange's equations for hybrid systems are derived.
Abstract: This paper is concerned with the general motion of a flexible body in space. Using the extended Hamilton’s principle for distributed systems, standard Lagrange’s equations for hybrid systems are first derived. Then, the equations for the rigid-body motions are transformed into a symbolic vector form of Lagrange’s equations in terms of general quasi-coordinates. The hybrid Lagrange’s equations of motion in terms of general quasi-coordinates are subsequently expressed in terms of quasi-coordinates representing rigid-body motions. Finally, the second-order Lagrange’s equations for hybrid systems are transformed into a set of state equations suitable for control. An illustrative example is presented.

Journal ArticleDOI
TL;DR: In this article, Boussinesq equations describing one-dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub- and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope.
Abstract: Boussinesq equations describing one-dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub- and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope. For this purpose the MacCormack (second-order accurate in space and time) and two-four (second-order accurate in-time and fourth-order in space) explicit finite-difference schemes are used to solve the governing equations subject to specified end conditions until a steady state is reached. The inclusion of initial and boundary conditions is discussed, and the importance of the Boussinesq terms is investigated. Complete test results for a range of Froude numbers are presented that may be used by other researchers for the verification of mathematical models. A comparison of the computed measured results shows that the agreement between them is satisfactory for the fourth-order finite-difference scheme although the second-order scheme does not accurately predict the location of the jump. These simulations show that the Boussinesq terms have little effect in determining the location of the hydraulic jump.

Journal ArticleDOI
TL;DR: In this paper, two nondegenerate quantum levels coupled off-diagonally and linearly to a bath of quantum-mechanical harmonic oscillators are considered, and the rate constant for the relaxation of nonequilibrium population distributions is 1/T1, defined as the sum of the rate constants in the master equation.
Abstract: Two nondegenerate quantum levels coupled off‐diagonally and linearly to a bath of quantum‐mechanical harmonic oscillators are considered. In the weak‐coupling limit one finds that the equations of motion for the reduced density‐matrix elements separate naturally into two uncoupled pairs of linear equations for the diagonal and off‐diagonal elements, which are known as the Bloch equations. The equations for the populations form the simplest two‐component master equation, and the rate constant for the relaxation of nonequilibrium population distributions is 1/T1, defined as the sum of the ‘‘up’’ and ‘‘down’’ rate constants in the master equation. Detailed balance is satisfied for this master equation in that the ratio of these rate constants is equal to the ratio of the equilibrium populations. The relaxation rate constant for the off‐diagonal density‐matrix elements is known as 1/T2. One finds that this satisfies the well‐known relation 1/T2=1/2T1. In this paper the weak‐coupling limit is transcended by de...

Journal ArticleDOI
TL;DR: In this article, the role of the cutoff frequency, ~2, in the AL equation of motion has been analyzed, and it has been shown that an equation independent of 12 may be achieved by working to or working to 12.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the Jaynes-Cummings model with cavity damping in the rotated-wave approximation and found that the initially one-peak quasiprobability function splits into two peaked functions counterrotating in the complex plane and, depending on the damping constant, spiraling into the origin.
Abstract: The Jaynes-Cummings model with cavity damping is investigated in the rotated-wave approximation. First we introduce six appropriate combinations of the matrix elements of the density operator, which are still operators with respect to the light field. With the help of the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)] the equations of motion for the density operator transform to six coupled partial-differential equations. By expanding the quasiprobability distributions into two suitable sets, we obtain six tridiagonally coupled differential equations for the expansion coefficients, which are solved by a Runge-Kutta method. Starting with an initial coherent state of the cavity field and the atom in its upper state, we find that the initially one-peak quasiprobability function splits into two peaked functions counterrotating in the complex plane and, depending on the damping constant, spiraling into the origin. Revivals of the inversion oscillation are found for those times, when the two peaks collide. The time dependence of the inversion and the intensity as well as some special distributions of interest are also discussed.

Book
27 May 1991
TL;DR: In this article, the authors introduce elasto-dynamics: linear oscillators and virtual work methods in dynamics, and the nature of the inertia forces and the mass matrix.
Abstract: 1. Introduction to elasto-dynamics: linear oscillators. 2. The equations of motion and virtual work methods in dynamics. 3. The nature of the inertia forces and the mass matrix. 4. The natural vibrations of undamped systems. 5. Free vibrations of undamped systems. 6. Forced vibrations of undamped systems. 7. The nature of damping forces modal damping. 8. Random vibrations of modally damped systems. 9. Dynamic analysis of structures with arbitrary viscous damping. 10. Direct integration methods for the equation of dynamic equilibrium. 11. Aspects of non-linear structural dynamics.

Journal ArticleDOI
Ömer Morgül1
TL;DR: In this article, a flexible structure modeled as a rigid body which rotates in inertial space is considered, where a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other.
Abstract: The author considers a flexible structure modeled as a rigid body which rotates in inertial space; a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other. It is assumed that the flexible beam performs only planar motion. The equations of motion are obtained by using free body diagrams. Two control problems are posed, namely the orientation and stabilization of the system. It is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above. The proofs are obtained by using the energy of the system as a Lyapunov functional. >

Journal ArticleDOI
TL;DR: In this paper, the authors introduced metric independent field theories, which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold, and have invariance of solutions of field equations under arbitrary functional redefinitions of the field quantities.
Abstract: Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the independent variables, one has invariance of solutions of the field equations under arbitrary functional redefinitions of the field quantities. Among the many interesting properties of these new models is the existence of a hierarchical structure which is illustrated by the following result. Given an arbitrary Lagrangian, dependent only upon first derivatives of the field, and homogeneous of weight one, an iterative procedure for calculating a sequence of equations of motion is discovered, which ends with a universal, possibly integrable equation, which is independent of the starting Lagrangian. A generalisation to more than one field is given.

Journal ArticleDOI
TL;DR: In this paper, a first-order system of conservation laws for finite deformation in solids, described its characteristic structure, and use this analysis to develop a second-order numerical method for problems involving finite deformations and plasticity.
Abstract: In this paper we develop a first-order system of conservation laws for finite deformation in solids, describe its characteristic structure, and use this analysis to develop a second-order numerical method for problems involving finite deformation and plasticity. The equations of mass, momentum, and energy conservation in Lagrangian and Eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy, as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient. Particular attention is paid to the influence of a curl constraint on the deformation gradient, so that the characteristic speeds transform properly between the two frames of reference. Next, we consider models in rate-form for isotropic elastic-plastic materials with work-hardening, and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion. In spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric, we still find that the characteristic speeds are always real for elastic behavior, and essentially always real for plastic response. These results allow us to construct a second-order Godunov method for the computation of three-dimensional displacement in a one-dimensional material viewed in the Lagrangian frame of reference. We also describe a technique for the approximate solution of Riemann problems in order to determine numerical fluxes in this algorithm. Finally, we present numerical examples of the results of the algorithm.

Journal ArticleDOI
TL;DR: Experiments using a vibrating tip close to a solid surface have shown a bistable behavior of the motion as mentioned in this paper, which can be interpreted in terms of perturbed harmonic oscillators both numerically and analytically.
Abstract: Experiments using a vibrating tip close to a solid surface have shown a bistable behavior of the motion These measurements have been interpreted in terms of perturbed harmonic oscillators both numerically and analytically

Journal ArticleDOI
TL;DR: In this paper, the authors consider corrections to Einstein gravity arising from the inclusion of Lorentz Chern-Simons terms, as well as Gauss-Bonnet terms, in a theory containing dilatons and Kalb-Ramond axions.

Journal ArticleDOI
TL;DR: In this article, a Lagrangian stochastic model for the motion of heavy particles was developed by coupling the Stokes equations of motion of a particle in a turbulent flow.
Abstract: A Lagrangian stochastic model for the motion of heavy particles has been developed by coupling a stochastic model for the motion of fluid elements to the Stokes equations of motion of a particle in a turbulent flow. The effects of crossing trajectories and continuity are incorporated by generalising Csanady's (1963) ideas developed for stationary homogeneous turbulence; effects of turbulence inhomogeneity and nonstationarity are embodied in the stochastic model for the fluid motion.

Journal ArticleDOI
TL;DR: In this paper, a method for eliminating the higher time derivatives directly on the Lagrangian level is presented, which clarifies the meaning of using the lower-order equations of motion in higher-order terms in a Lagrangians.
Abstract: Single‐time Lagrangians are treated in this paper, describing the dynamics of systems of point particles, which are given as formal power series in some ordering parameter and which may contain higher time derivatives in all terms but the leading one. An efficient method for eliminating the higher time derivatives directly on the Lagrangian level is presented. This method clarifies the meaning of using the lower‐order equations of motion in higher‐order terms in a Lagrangian. The method consists of an iterative use of ‘‘contact’’ transformations in the jet prolongation of the extended configurations space and is called ‘‘the method of redefinition of position variables.’’ Several examples from electrodynamics and relativistic gravity are treated explicitly.

Journal ArticleDOI
TL;DR: In this paper, the dynamics equations governing the motion of mechanical systems composed of rigid bodies coupled by holonomic and nonholonomic constraints are derived based on a natural orthogonal complement of the matrix associated with the velocity constraint equations written in linear homogeneous form.
Abstract: The dynamics equations governing the motion of mechanical systems composed of rigid bodies coupled by holonomic and nonholonomic constraints are derived. The underlying method is based on a natural orthogonal complement of the matrix associated with the velocity constraint equations written in linear homogeneous form. The method is applied to the classical example of a rolling disk and an application to a 2-dof Automatic Guided Vehicle is outlined.

Journal ArticleDOI
TL;DR: In this paper, a semi-Lagrangian semi-implicit approach was proposed to produce medium-range (5-day) forecasts using time-steps that are far larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian model.
Abstract: It has previously been shown that semi-Lagrangian schemes can be applied to spectral models of the shallow-water equations using large time-steps (e.g., see Ritchie 1988). The present study considers the extension of this work to a multilevel spectral primitive-equations model. As a first step, an Eulerian vorticity-divergence spectral model is converted to an Eulerian model based on a vector momentum form of the equation of motion. From the latter, several semi-Lagrangian models are prepared: one using an interpolating semi-Lagrangian treatment of advection in the horizontal (referred to as 2DISL) while retaining Eulerian advection in the vertical, another using a 3-dimensional interpolating semi-Lagrangian formulation (referred to as 3DISL), and another which combines the 2DISL scheme in the horizontal and a non-interpolating semi-Lagrangian treatment in the vertical (referred to as NISLV). Medium-range intercomparison experiments are performed using models that include simple physical parametrizations. It is shown that the semi-Lagrangian semi-implicit approach can be applied accurately and stably to produce medium-range (5-day) forecasts using time-steps that are far larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian model. The NISLV version is found to be more accurate than the 3DISL one which apparently has excessive damping in the vicinity of the tropopause, where all the model fields change abruptly in the vertical.

01 Jan 1991
TL;DR: In this paper, the authors present a simulation of a wheel-and-rail system on a rail track and demonstrate the advantages of the DAE-formulation in railway vehicle dynamics.
Abstract: The multibody system approach provides an efficient tool for the analysis of mechanical systems arising in vehicle dynamics. The computer-aided formalisms generate the equations of motion as a system of differential-algebraic equations (DAEs). A short review of their solution theory and of the implications for the numerical integration is presented. The available integr. methods are describ. and a method for the computation of consistent initial values is introduced. The investigation of a wheelset moving on a rail track demonstrates the advantages of the DAE-formulation in railway vehicle dynamics. Thus an alternative to the usual state space form approach is provided for this class of problems. The computation of static equilibrium solutions of the wheelset yields consistent initial values and allows an analysis of wheel and rail design. Finally, a numerical integration determines the limit cycle behaviour of the wheelset in accordance with measurement on a hardware model.

Journal ArticleDOI
TL;DR: In this paper, the problem of minimizing the total characteristic velocity of a spacecraft having linear equations of motion and finitely many instantaneous impulses that result in jump discontinuities in velocity is considered.
Abstract: The problem of minimizing the total characteristic velocity of a spacecraft having linear equations of motion and finitely many instantaneous impulses that result in jump discontinuities in velocity is considered. Fixed time and fixed end conditions are assumed. This formulation is flexible enough to allow some of the impulses to be specifieda priori by the mission planner. Necessary and sufficient conditions for solution of this problem are found without using specialized results from control theory or optimization theory. Solution of the two-point boundary-value problem is reduced to a problem of solving a specific set of equations. If the times of the impulses are specified, these equations are at most quadratic. Although this work is restricted to linear equations, there are situations where it has potential application. Some examples are the computation of the velocity increments of a spacecraft near a real or fictitious satellite or space station in a circular or more general Keplerian orbit. Another example is the computation of maneuvers of a spacecraft near a libration point in the restricted three-body problem.