Showing papers on "Inertia published in 1995"

Gravitation and Inertia

Abstract: PrefaceChart of Main Topics1A First Tour12Einstein Geometrodynamics133Tests of Einstein Geometrodynamics874Cosmology, Standard Models, and Homogeneous Rotating Models1855The Initial-Value Problem in Einstein Geometrodynamics2696The Gravitomagnetic Field and Its Measurement3157Some Highlights of the Past and a Summary of Geometrodynamics and Inertia384Mathematical Appendix403Symbols and Notations437Author Index445Subject Index of Mathematical Appendix455Subject Index461Fundamental and Astronomical Constants and Units493

Mach's Principle: From Newton's Bucket to Quantum Gravity.

Abstract: This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time,space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity.

Computer simulations of Brownian motion of complex systems

Abstract: Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models; firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.

Nonlinear modelling of marine vehicles in 6 degrees of freedom

Abstract: In this paper a unified framework for vectorial parametrisation of inertia, Coriolis and centrifugal, and hydrodynamic added mass forces for marine vehicles in 6 degrees of freedom (DOF) is presented. Emphasises is placed on representing the 6 DOF nonlinear marine vehicle equations of motion in vector form satisfying certain matrix properties like symmetry, skew-symmetry and positive definiteness. For marine vehicles, this problem was first addresed by Fossen [1]. The proposed representations in this paper are based on extensions of this work. The main results are presented as two theorems. The first theorem is derived by applying Newton's equations whereas the second theorem reviews the main results of Sagatun and Fossen [6] where the Lagrangian formalism is applied.

Imbalance compensation and automation balancing in magnetic bearing systems using the Q-parameterization theory

Abstract: The problem caused by imbalance in rotating machinery can be solved using actively controlled magnetic bearing systems. There are two methods to solve this problem using feedback control: 1) compensate for the imbalance forces by generating opposing forces on the bearing surface; and 2) make the rotor rotate around its axis of inertia so no imbalance forces will be generated. The dynamics of the magnetic bearing are described in state-space form using airgap displacement, velocity, and airgap flux as state variables. The system which is unstable in nature is stabilized using the Q-parameterization theory. To compensate for the imbalance disturbance forces, the controller Q-parameter is chosen such that rejection of sinusoidal disturbances is achieved. To achieve automatic balancing, the imbalance is assumed as a sinusoidal noise in the measured signal, and the controller Q-parameter is chosen such that rejection of sinusoidal noise is achieved. Simulation results are presented and show the robustness of the proposed controllers and that the rejection of sinusoidal disturbances is achieved. The rotation of the rotor around its axis of inertia is also achieved. >

Seismic bearing capacity of foundation on cohesionless soil

Abstract: The seismic bearing capacity of a strip-surface foundation resting on a Mohr-Coulomb material is evaluated. The upper-bound theorem of the yield design theory is used to obtain an estimate of the ultimate load. The loading parameters consist of a normal and tangential force applied to the foundation and of inertia forces developed within the soil volume. The classical Prandtl-like mechanism is used to show that the reduction in the bearing capacity is mainly caused by the load inclination; the consideration of inertia forces within the soil is only responsible for a decrease in the bearing capacity that is at least an order of magnitude smaller than the one caused by the load inclination. It is therefore concluded that, from a practical engineering standpoint, the soil-inertia forces can be neglected.

The unsteady motion of solid bodies in creeping flows

Abstract: In treating unsteady particle motions in creeping flows, a quasi-steady approximation is often used, which assumes that the particle’s motion is so slow that it is composed of a series of steady states. In each of these states, the fluid is in a steady Stokes flow and the total force and torque on the particle are zero. This paper examines the validity of the quasi-steady method. For simple cases of sedimenting spheres, previous work has shown that neglecting the unsteady forces causes a cumulative error in the trajectory of the spheres. Here we will study the unsteady motion of solid bodies in several morecomplex flows: the rotation of an ellipsoid in a simple shear flow, the sedimentation of two elliptic cylinders and four circular cylinders in a quiescent fluid and the motion of an elliptic cylinder in a Poiseuille flow in a two-dimensional channel. The motion of the fluid is obtained by direct numerical simulation and the motion of the particles is determined by solving their equations of motion with solid inertia taken into account. Solutions with the unsteady inertia of the fluid included or neglected are compared with the quasi-steady solutions. For some flows, the effects of the solid inertia and the unsteady inertia of the fluid are important quantitatively but not qualitatively. In other cases, the character of the particles’ motion is changed. In particular, the unsteady effects tend to suppress the periodic oscillations generated by the quasi-steady approximation. Thus, the results of quasi-steady calculations are never uniformly valid and can be completely misleading. The conditions under which the unsteady effects at small Reynolds numbers are important are explored and the implications for modelling of suspension flows are addressed.

A motion control strategy based on equivalent mass matrix in multidegree-of-freedom manipulator

Abstract: This paper describes a decoupling motion control strategy based on an equivalent mass matrix in operational space. In the conventional approach, the equivalent mass matrix is defined as a function of Jacobian matrix and inertia of manipulator. Therefore, it is difficult to know the variation of the equivalent mass matrix precisely and to select it arbitrarily. This makes it difficult to realize the decoupling motion controller in the operational space. To improve the above problem, the authors introduce a robust control strategy based on a disturbance observer. In the observer-based approach, the equivalent mass matrix is determined arbitrarily independently of configuration and inertia variation of the manipulator. First, the equivalent mass matrix based on robust control is derived. Second, a simplification method of an operational space controller is discussed by using the equivalent mass matrix. Several experimental results are shown to confirm the validity of the proposed methods. >

Deformation of a graphic object to emphasize effects of motion

Abstract: A three-dimensional graphic object appearing in an animation is deformed to simulate the effects of motion on the object. A user can selectively apply a stretch, yield, or flex deformation effect to the control vertices of the object, to change the shape of the object as a function of any of a linear velocity, angular velocity, linear acceleration, or angular acceleration of the object. Various other parameters for each of these deformation effects can also be selected and set by the user, including a sensitivity to the motion in generating the deformation and a maximum deformation. The flex deformation can selectively be set to either a linear or curved profile, simulating the effect of friction applied by the environment on one or more surfaces of the object. The stretch deformation can selectively be set to either a constant or a free volume to simulate the effect of inertia, causing a body to elongate or shrink in the direction of the movement. The yield deformation can be set either a linear or curved profile, simulating the displacement of an object's internal matter toward one end that occurs, relative to the direction of the object's motion, i.e., causing one end to bulge. For each control vertex on the object, an effect offset is determined for each motion component and for each selected deformation effect. The sum of the effect offsets for the control vertex represents a total offset that is added to the original control vertex to determine a deformed control vertex. This step is repeated for all control vertices to produce the deformed object.

EHD Analysis, Including Structural Inertia Effects and a Mass-Conserving Cavitation Model

Abstract: The dynamic behavior of two elastic connecting-rod bearings is studied. The Newton-Raphson method and 8-node isoparametric elements for the lubrication analysis are used. For the structural analysis, 3-D elasticity assumptions are made and 20 nodes isoparametric elements are used. Inertia forces due to the kinematics of the structure are incorporated with the effects of the hydrodynamic pressures in the elastic deformations of the bearing. Comparisons with Goenka‘s results are presented for the General Motors connecting-rod bearing. A mass-conserving model used in conjunction with Murty‘s algorithm is presented for the transient evolution of the cavitation area. This model is applied for the EHD study of a Renault connecting-rod bearing.

Hybrid equations of motion for flexible multibody systems using quasicoordinates

Abstract: A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Finite Element Incremental Approach and Exact Rigid Body Inertia

Abstract: In the dynamics of multibody systems that consist of interconnected rigid and deformable bodies, it is desirable to have a formulation that preserves the exactness of the rigid body inertia. As demonstrated in this paper, the incremental finite element approach, which is often used to solve large rotation problems, does not lead to the exact inertia of simple structures when they rotate as rigid bodies. Nonetheless, the exact inertia properties, such as the mass moments of inertia and the moments of mass, of the rigid bodies can be obtained using the finite element shape functions that describe large rigid body translations by introducing an intermediate element coordinate system. The results of application of the parallel axis theorem can be obtained using the finite element shape functions by simply changing the element nodal coordinates. As demonstrated in this investigation, the exact rigid body inertia properties in case of rigid body rotations can be obtained using the shape function if the nodal coordinates are defined using trigonometric functions. The analysis presented in this paper also demonstrates that a simple expression for the kinetic energy can be obtained for flexible bodies that undergo large displacements without the need for interpolation of large rotation coordinates.

Finite element simulation of the inertia welding of two similar parts

Abstract: A complete thermo‐mechanical model for the simulation of the inertia welding process of two similar parts is described. The material behaviour is represented by an incompressible viscoplastic Norton—Hoff law in which the rheological parameters are dependent on temperature. The friction law was determined experimentally and depends on the prescribed pressure and the relative rotating velocity between the two parts. The mechanical problem is solved considering the virtual work principle including inertia terms. The computation of the three components of the velocity field such as radial, longitudinal and rotational velocity, in an axisymmetric approximation allows to take into account the torsional effects. The domain is updated based on a Lagrangian formulation. The non‐linear heat transfer equation with boundary conditions (convection, radiation and friction flux) is solved separately for each time step. Error estimators on mechanical and thermal computation are devised to adapt the mesh in an automatic w...

Fluid dynamic limitations on the performance of an electrorheological clutch

Abstract: We examine flow in a cylindrical electrorheological clutch and discuss the fluid dynamic and inertial effects which limit the speed of operation. Time-dependent solutions of the equation of motion are developed in which the fluid is treated as a homogeneous continuum obeying the Bingham plastic constitutive equation. Some approximations have to be made but the results give a realistic description of the acceleration in clutches of practical dimensions. The problem is also approached in an entirely different way by direct numerical integration using an alternative time-dependent model. There is agreement between the two methods and the results show that the fluid density and viscosity place an upper limit on the acceleration of the output rotor. This is only reached if very low moment of inertia rotors are used, otherwise the output hardware inertia is the limiting factor. Design formulae are developed to give a rough estimate for the fluid limited acceleration and to define the minimum output moment of inertia that can usefully be employed to give maximum available acceleration.

Dynamic simulation of the motion of capsules in pipelines

Abstract: In this paper we report results of two-dimensional simulations of the motion of elliptic capsules carried by a Poiseuille flow in a channel. The numerical method allows computation of the capsule motion and the fluid flow around the capsule, and accurate evaluation of the lift force and torque. Results show that the motion of a capsule which is heavier than the carrying fluid may be decomposed into three stages: initial lift-off, transient oscillations and steady flying. The behaviour of the capsule during initial lift-off and steady flying is analysed by studying the pressure and shear stress distributions on the capsule. The dominant mechanism for the lift force and torque is lubrication or inertia or a combination of the two under different conditions. The lift-off velocity for the ellipse in two dimensions is compared with experimental values for cylindrical capsules in pipes. Finally, the mechanisms of lift for capsules are applied to flying core flows, and it is argued that inertial forces are responsible for levitating heavy crude oil cores lubricated by water in a horizontal pipeline.

Pressure-driven flow of a thin viscous sheet

Abstract: Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.

The design of a vehicle inertia measurement facility

Abstract: This paper describes the design of a vehicle inertia measurement facility (VIMF) used to measure: (1) vehicle center of gravity position; (2) vehicle roll, pitch, and yaw mass moments of inertia; and (3) vehicle roll/yaw mass product of inertia. The rationale for general design decisions and the methods used to arrive at the decisions are discussed. The design is inspired by the desire to have minimal measurement error and short test time. The design was guided by analytical error analyses of the contributions of individual system errors to the overall measurement error. A National Highway Traffic Safety Administration (NHTSA) database of center of gravity position and mass moment of inertia data for over 300 vehicles was used. This database was used in conjunction with the error analyses to design various VIMF components such as the roll and yaw spring sizes. This provides for a design that yields good experimental repeatability for the full range of lightvehicles that can be tested on the VIMF. The paper also discusses aspects of the VIMF software, for example: (a) the analytical curve fitting; and (b) the error checking of results. Results from the VIMF for two calibration fixtures are presented and compared to the computed center of gravity position and inertia values. For the covering abstract of the conference see IRRD 875861.

Settling and asymptotic motion of aerosol particles in a cellular flow field

Abstract: This paper presents a proof that given a dilute concentration of aerosol particles in an infinite, periodic, cellular flow field, arbitrarily small inertial effects are sufficient to induce almost all particles to settle It is shown that when inertia is taken as a small parameter, the equations of particle motion admit a slow manifold that is globally attracting The proof proceeds by analyzing the motion on this slow manifold, wherein the flow is a small perturbation of the equation governing the motion of fluid particles The perturbation is supplied by the inertia, which here occurs as a regular parameter Further, it is shown that settling particles approach a finite number of attracting periodic paths The structure of the set of attracting paths, including the nature of possible bifurcations of these paths and the resulting stability changes, is examined via a symmetric one-dimensional map derived from the flow

Stability of Masonry Walls Subjected to Seismic Transverse Forces

Abstract: The stability condition of masonry walls subjected to seismic transverse forces is investigated by translating the problem into the analysis of a fixed–free ended prismatic column undergoing static horizontal forces equivalent to the maximum inertia actions. The column is assumed to be made of a no-tension material, with a linear stress-strain law in compression. The solution is achieved by a numerical model in which the column is ideally divided into a sufficiently high number of elements, each with uniform curvature. With reference to the deformed shape corresponding to a given load condition, this approach allows the stress and strain characteristic quantities of a cross section to be expressed recursively, and the stability domain to be defined in dimensionless terms. In the general case of a column subjected to its own weight, to a concentrated eccentric compressive load acting at the top, and to the related horizontal inertia forces, the results show that large-displacement effects, due to the mater...

Engineering Mechanics Dynamics

Abstract: 1. Engineering and Mechanics. Engineering and Mechanics. Learning Mechanics. Fundamental Concepts. Units. Newtonian Gravitation. 2. Motion of a Point. Position, Velocity, and Acceleration. Straight-Line Motion. Curvilinear Motion. 3. Force, Mass, and Acceleration. Newton's Second Law. Equation of Motion for the Center of Mass. Inertial Reference Frames. Applications. Orbital Mechanics. Numerical Solutions. 4. Energy Methods. Work and Kinetic Energy. Principle of Work and Energy. Work and Power. Work Done by Particular Forces. Potential Energy. Conservation of Energy. Conservative Forces. Relationship between Force and Potential Energy. 5. Momentum Methods. Principle of Impulse and Momentum. Conservation of Linear Momentum. Impacts. Angular Momentum. Mass Flows. 6. Planar Kinematics of Rigid Bodies. Rigid Bodies and Types of Motion. Rotation about a Fixed Axis. General Motions: Velocities. General Motions: Accelerations. Sliding Contacts. Moving Reference Frames. 7. Planar Dynamics of Rigid Bodies. Preview of the Equations of Motion. Momentum Principles for a System of Particles. Derivation of the Equations of Motion. Applications. Numerical Solutions. Appendix: Moments of Inertia. 8. Energy and Momentum in Rigid-Body Dynamics. Principle of Work and Energy. Kinetic Energy. Work and Potential Energy. Power. Principles of Impulse and Momentum. Impacts. 9. Three-Dimensional Kinematics and Dynamics of Rigid Bodies. Kinematics. Euler's Equations. The Euler Angles. Appendix: Moments and Products of Inertia. 10. Vibrations 506 Conservative Systems. Damped Vibrations. Forced Vibrations. Appendix A. Review of Mathematics. Appendix B. Properties of Areas and Lines. Appendix C. Properties of Volumes and Homogeneous Objects. Appendix D. Spherical Coordinates. Appendix E. D'Alembert's Principle. Index.

A three-dimensional computation of the force and torque on an ellipsoid settling slowly through a viscoelastic fluid

Abstract: The orientation of an ellipsoid falling in a viscoelastic fluid is studied by methods of perturbation theory. For small fall velocity, the fluid's rheology is described by a second-order fluid model. The solution of the problem can be expressed by a dual expansion in two small parameters: the Reynolds number representing the inertial effect and the Weissenberg number representing the effect of the non-Newtonian stress. Then the original problem is split into three canonical problems: the zeroth-order Stokes problem for a translating ellipsoid and two first-order problems, one for inertia and one for second-order rheology. A Stokes operator is inverted in each of the three cases. The problems are solved numerically on a three-dimensional domain by a finite element method with fictitious domains, and the force and torque on the body are evaluated. The results show that the signs of the perturbation pressure and velocity around the particle for inertia are reversed by viscoelasticity. The torques are also of opposite sign: inertia turns the major axis of the ellipsoid perpendicular to the fall direction; normal stresses turn the major axis parallel to the fall. The competition of these two effects gives rise to an equilibrium tilt angle between 0° and 90° which the settling ellipsoid would eventually assume. The equilibrium tilt angle is a function of the elasticity number, which is the ratio of the Weissenberg number and the Reynolds number. Since this ratio is independent of the fall velocity, the perturbation results do not explain the sudden turning of a long body which occurs when a critical fall velocity is exceeded. This is not surprising because the theory is valid only for slow sedimentation. However, the results do seem to agree qualitatively with ‘shape tilting’ observed at low fall velocities.

Negative inertia: a dynamic pointing function

Abstract: In-keyboard isometric joysticks can give better pcrforrnancc than mice for mixed typing/pointing tasks. The continuing challcngc is to improve such devices to the point that they arc preferable even for pure pointing tasks. Previous work has improved joystick performance by considering user perception and motor skills. This paper considers the dynamics of the pointing operation. A dynamic transfer function for an isometric joystick is described which amplifies changes in the applied force to increase rcsponsivcncss without loss of control. User tests show a 7.8k3.5°/0 pcrfonnancc improvement over a standard non-dynamic joystick. This feature has been incorporated into the TrackPoint 111from IBM.

Gravitation and Inertia

Abstract: PrefaceChart of Main Topics1A First Tour12Einstein Geometrodynamics133Tests of Einstein Geometrodynamics874Cosmology, Standard Models, and Homogeneous Rotating Models1855The Initial-Value Problem in Einstein Geometrodynamics2696The Gravitomagnetic Field and Its Measurement3157Some Highlights of the Past and a Summary of Geometrodynamics and Inertia384Mathematical Appendix403Symbols and Notations437Author Index445Subject Index of Mathematical Appendix455Subject Index461Fundamental and Astronomical Constants and Units493

Lagrange and Newton-Euler dynamic modeling of a gear-driven robot manipulator with inclusion of motor inertia effects

Abstract: This paper is aimed at presenting the dynamic model of a gear-driven rigid robot manipulator. The dynamic effects of the motion of the motors driving the joints through gears are analyzed. A complete model is derived using the Lagrange formulation in which the contributions of rotor inertias and rotor-link interactions are evidenced. The resulting equations of motion are shown to be linear in terms of a suitable set of dynamic parameters for the augmented links (links with motors). These are utilized for model derivation using the recursive Newton-Euler formulation. The explicit dynamic model for an elbow manipulator is developed.

Nonlinear Response of a Taut String to Longitudinal and Transverse End Excitation

Abstract: The nonlinear response of a taut string to an end excitation with components both parallel and transverse to its axis is theoretically and experimentally studied A model for the transverse vibration of the string is developed by neglecting its longitudinal inertia The method of multiple scales is applied directly to the governing partial-differential equations and boundary conditions A continuation method is then employed to determine the constant amplitude and phase solutions and their stability Resonant responses are predicted to occur simultaneously in as many as three modes An experimental study is conducted and the results are found to be in good agreement with the theory

Non-Darcy natural convection from a vertical wavy surface in a porous medium

Abstract: We examine the combined effect of spatially stationary surface waves and the presence of fluid inertia on the free convection induced by a vertical heated surface embedded in a fluid-saturated porous medium. We consider the boundary-layer regime where the Darcy-Rayleigh number, Ra, is very large, and assume that the surface waves have O(1) amplitude and wavelength. The resulting boundary-layer equations are found to be nonsimilar only when the surface is nonuniform and inertia effects are present; self-similarity results when either or both effects are absent. Detailed results for the local and global rates of heat transfer are presented for a range of values of the inertia parameter and the surface wave amplitude.