Showing papers on "Inertia published in 1993"

Dynamic and loaded impedance components in the maintenance of human arm posture

Abstract: The postural stiffness of the human arm has previously been estimated by displacing the hand from a series of equilibrium positions and correlating the resultant displacements and restoring forces. We extend this experimental methodology to include measurement of dynamic components of impedance. The stiffness-damping-mass characteristics are represented numerically as matrices and graphically as ellipses characterized by size, shape, and orientation. The latter depict the predominant nonrotational component of the impedance force fields. The results suggest: (1) joint damping is related to both joint stiffness and joint inertia; and (2) two-joint impedances, i.e., impedances associated with muscles connected across both the elbow and shoulder joints, play a relatively smaller role in damping than in stiffness. The ability to modulate stiffness in the face of initial static bias forces, i.e., "loading", is also examined. We observe regular shifts in the human arm endpoint's "spring center" corresponding to the bias force directions and magnitudes. >

Internal force-based impedance control for cooperating manipulators

Abstract: An internal force-based impedance control scheme for cooperating manipulators is introduced which controls the motion of the objects being manipulated and the internal force on the objects. The controller enforces a relationship between the velocity of each manipulator and the internal force on the manipulated objects. Each manipulator is directly given the properties of an impedance by the controller; thus, eliminating the gain limitation inherent in the structure of previously proposed schemes. The controller uses the forces sensed at the robot end effectors to compensate for the effects of the objects' dynamics and to compute the internal force using only kinematic relationships. Thus, knowledge of the objects' dynamics is not required. Stability of the system is proven using Lyapunov theory and simulation results are presented validating the proposed concepts. The effect of computational delays in digital control implementations is analyzed vis-a-vis stability and a lower bound derived on the size of the desired manipulator inertia relative to the actual manipulator endpoint inertia. The bound is independent of the sample time.

Dispersion of heavy particles by turbulent motion

Abstract: Accurate prediction of heavy particle dispersion in turbulent flows requires a simultaneous consideration of particle's inertia and particle's drift velocity. A mathematically simple and physically comprehensive analysis was developed to solve the dispersion statistics of heavy particles in a homogeneous and isotropic turbulent flow. Normalized particle diffusivity, rms fluctuating velocity, and Lagrangian integral time were related by algebraic equations to three dimensionless parameters: the inertia parameter, the drift parameter, and the turbulence structure parameter. When the drift parameter is large, dispersion scales are very sensitive to the inertia parameter. Heavy particles were found to disperse faster than fluid elements if the inertia parameter controls the dispersion and slower than fluid elements if the drift parameter governs the dispersion. This finding explains previous “contradictory” dispersion data observed in experimental measurements. Not only the particle time respective b...

An Explicit Inertial Method for the Simulation of Viscoelastic Flow: An Evaluation of Elastic Effects on Diapiric Flow in Two- and Three- Layers Models

Abstract: The explicit finite-difference approach used in the FLAC (Fast Lagrangian Analysis of Continua) algorithm is combined with a marker technique for solving multi-component problems. A remeshing procedure is introduced in order to follow the viscoelastic flow when a Lagrangian mesh is too distorted. Dimension analysis for the case of Maxwell rheology is made. The adaptive density scaling for increasing time step of explicit scheme and influence of inertia are explained.

The Continuum Mechanics of Coherent Two-Phase Elastic Solids with Mass Transport

Abstract: We develop a theory for the dynamics of an interface in a two-phase elastic solid with kinetics driven by mass transport and stress. We consider a two-phase system consisting of bulk regions separated by a sharp interface endowed with energy and capable of supporting force. Our discussion is based on balance laws for mass and force in conjunction with a version of the second law-appropriate to a mechanical system out of equilibrium-which we use to develop a suitable constitutive theory for the interface. It is assumed that mass transport is characterized by the bulk diffusion of a single independent species; we neglect mass diffusion within the interface; limit our discussion to a continuous chemical potential and to a coherent interface; neglect the elasticity of the interface; and consider only infinitesimal deformations, neglecting inertia. We show that the field equations and free-boundary conditions can be developed in a simple manner in terms of the diffusion potential and its time derivatives, as opposed to the usual formulation in terms of concentration. Natural consequences of the thermodynamic framework are Lyapunov functions for the resulting evolution problems. This leads to a hierarchy of variational principles that should describe the equilibrium shapes of misfitting particles as well as possible microstructures that might form; these principles are applicable both in the absence and presence of an applied stress.

Basic consideration of vibration suppression and disturbance rejection control of n-inertia system using SFLAC (state feedback and load acceleration control)

Abstract: SFLAC (state feedback and load acceleration control) is proposed for vibration suppression and disturbance rejection control of n-inertia system. An n-inertia system is a model of a steel rolling mill, flexible arm, large scale space structure, etc., and its control will be an important problem in the future motion control. The main idea of SFLAC is to control the load acceleration which can be estimated by the state observer including the disturbance estimation. A simple PI speed controllers and SFLAC based on the reduction models using 2 and 3 inertia moments are designed. The effectiveness of SFLAC is demonstrated showing some simulation results. >

Nonlinear Analysis of Automotive Hydraulic Engine Mount

Abstract: Nonlinear properties of a generic hydraulic mount with an inertia track are identified and characterized by using experimental and analytical approaches. A low-frequency lumped-parameter mathematical model of the hydraulic mount is developed over 1 to 50 Hz, based on the measured nonlinear system parameters such as the steadystate inertia track fluid resistances and fluid chamber compliances. New experiments specifically designed for this study are also described. The effect of temperature on the mount dynamic properties is discussed briefly

Sedimentation of particles in polymer solutions

Abstract: In this paper, we present detailed and systematic experimental results on the sedimentation of solid particles in aqueous solutions of polyox and polyacrylamide, and in solutions of polyox in glycerin and water. The tilt angles of long cylinders and flat plates falling in these viscoelastic liquids were measured. The effects of particle length, particle weight, particle shape, liquid properties and liquid temperature were determined. In some experiments, the cylinders fall under gravity in a bed with closely spaced walls. No matter how or where a cylinder is released the axis of the cylinder centres itself between the close walls and falls steadily at a fixed angle of tilt with the horizontal. A discussion of tilt angle may be framed in terms of competition between viscous effects, viscoelastic effects and inertia. When inertia is small, viscoelasticity dominates and the particles settle with their broadside parallel or nearly parallel to the direction of fall. Normal stresses acting at the corners of rectangular plates and squared-off cylinders with flat ends cause shape tilting from the vertical. Cylinders with round ends and cone ends tilt much less in the regime of slow flow. Shape tilting is smaller and is caused by a different mechanism to tilting due to inertia. When inertia is large the particles settle with their broadside perpendicular to the direction of fall. The tilt angle varies continuously from 90° when viscoelasticity dominates to 0° when inertia dominates. The balance between inertia and viscoelasticity was controlled by systematic variation of the weight of the particles and the composition and temperature of the solution. Particles will turn broadside-on when the inertia forces are larger than viscous and viscoelastic forces. This orientation occurred when the Reynolds number Re was greater than some number not much greater than one in any case, and less than 0.1 in Newtonian liquids and very dilute solutions. In principle, a long particle will eventually turn its broadside perpendicular to the stream in a Newtonian liquid for any Re > 0, but in a viscoelastic liquid this turning cannot occur unless Re > 1. Another condition for inertial tilting is that the elastic length λU should be longer than the viscous length ν/U where U is the terminal velocity, ν is the kinematic viscosity and λ = ν/c2 is a relaxation time where c is the shear wave speed measured with the shear wave speed meter (Joseph 1990). The condition M = U/c > 1 is provisionally interpreted as a hyperbolic transition of solutions of the vorticity equation analogous to transonic flow. Strong departure of the tilt angle from θ = 90° begins at about M = 1 and ends with θ = 0° when 1 < M < 4.

Constitutive laws for high-velocity frictional sliding and their influence on stress drop during unstable slip

Abstract: The Dieterich-Ruina state-variable friction laws do a good job describing results of rock friction experiments, and fault models based on them are able to mimic natural seismicity in many respects. To be useful for modeling earthquakes, high velocities must be successfully modelled. Ruina gave a formula for steady state frictional strength with a constant (usually negative) slope on a logarithmic plot that does not agree with recent observations of friction of a variety of materials at velocities greater than 30 to 100 μms−1. This steady state function, termed the “log-linear function,” with inertia neglected, does not recover from instability and, consequently, cannot give predictions of stress drop or peak velocities during unstable slip. Adding inertia yields stress drops that are too large to match experimental observations. This paper explores the consequences for unstable slip when inertia is considered and when the steady state function is altered at high velocity. Two steady state functions are considered: one that has no dependence on velocity at high slip velocity (“zero-slope”) and one that has a positive velocity dependence at high velocity (“positive-slope”). Inclusion of inertia and use of these modified steady state functions improve the results of simulations in terms of qualitatively reproducing many aspects of unstable sliding, but the positive-slope function yields the best quantitative agreement with experimental observations. Use of the modified steady state functions predicts that stress drop during unstable sliding should decrease with increasing loading velocity and at sufficiently high load point velocity there will be a transition to stable sliding, a result that is observed experimentally.

Study of the effect of leg inertia in Stewart platforms

Abstract: The inertia effect of all the leg rotations in a Stewart platform is studied. The dynamics of the legs are decoupled from that of the mobile plate so that the actuating force for moving the legs can be computed separately from that for moving the mobile plate. This enables the evaluation of the effect of leg inertia. Dynamic mobile simulation based on the decoupled dynamics formulation is discussed. >

Method and device for generating an input command for a motion control system

Abstract: A method and device of achieving motion cycle time reduction that takes motor capabilities, load inertia and gravity into account and, at the same time, produces acceptable tool tip vibration upon stopping. This cycle time reduction is especially applicable to short motions of a robot where the entire motion consists of acceleration and deceleration and there is no constant velocity region. The method and device provide open loop limiting factors for axis jerk, acceleration and velocity, taking into account robot position, payload and inertia.

Dynamic Characteristics of Liquid Motion in Partially Filled Tanks of a Spinning Spacecraft

Abstract: This paper presents a boundary-layer model to predict dynamic characteristics of liquid motion in partially filled tanks of a spinning spacecraft. The solution is obtained by solving three boundary-value problems: an inviscid fluid problem, a boundary-layer problem, and a viscous correction problem. The boundary-layer solution is obtained analytically, and the solutions to inviscid and viscous correction problems are obtained by using finite element methods. The model has been used to predict liquid natural frequencies, mode shapes, damping ratios, and nutation time constants for a spinning spacecraft. The results show that liquid motion in general will contain significant circulatory motion due to Coriolis forces except in the first azimuth and first elevation modes. Therefore, only these two modes can be represented accurately by equivalent pendulum models. The analytical results predict a sharp drop in nutation time constants for certain spacecraft inertia ratios and tank fill fractions. This phenomenon was also present during on-orbit liquid slosh tests and ground air-bearing tests. I. Introduction A RECENT trend in geosynchronou s spacecraft design is to use liquid apogee motors, which results in liquid constituting almost half of the spacecraft mass during transfer orbit. In these spacecraft, liquid motion significantly influences the spacecraft attitude stability and control. LEAS AT, a geosynchronous spacecraft with liquid apogee motor, launched in September 1984, experienced attitude control motion instability1 during the pre-apogee injection phase, immediately following the activation of despin control. The instability was found to be the result of interaction between liquid lateral sloshing modes and the attitude control. This experience demonstrated that the analysis of dynamic interaction between liquid slosh motion and attitude control is critical in the attitude control design of these spacecraft. To perform this analysis, accurate determination of liquid dynamic characteristics, such as natural frequencies, mode shapes, damping, and modal masses becomes important. Accurate prediction of liquid dynamic characteristics is, however, a difficult problem because of the complexity of the hydrodynamical equations of motion. Several investigators have analyzed the fluid motion in rotating containers. Greenspan2 analyzed the transient motion during spin up of an arbitrarily shaped container filled with viscous imcompressible fluid. Stewartson3 developed a stability criterion for a spinning top containing fluid. This stability criterion was corrected by Wedemeyer 4 by considering fluid viscosity. Nayfeh and Meirovitch5 analyzed a spinning rigid body with a spherical cavity partially filled with liquid. Viscous effects are considered only for a boundary layer near the wetted surface. Hendricks and Morton6 analyzed the stability of a rotor partially filled with a viscous incompressible fluid. Stergiopoulous and Aldridge7 studied inertial waves in a partially filled cylindrical cavity during spin up. Pfeiffer8 introduced the concept of homogeneous vorticity to the problem of partially filled containers. El-Raheb and Wagner9 developed a finite element model based on a homogeneous vorticity as

Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints

Abstract: This paper presents a comprehensive, block-diagonal matrix formulation of the equations of motion of a system of hinge-connect ed flexible bodies undergoing large rotation and translation together with small elastic vibration. The formulation compensates for premature linearization of equations, associated with the customary treatment of small elastic displacement, by accounting for geometric stiffness due to inertia as well as interbody forces. The algorithm is first developed for a tree configuration and is then extended to the case of closed structural loops by cutting the loops and expressing all of the kinematical variables into terms dependent and free of constraint forces/torques. A solution procedure satisfying constraints is given.

Semiactive control of a vibrating system by means of electrorheological fluids

Abstract: A control scheme is designed for the purpose of suppression of vibratory motion of a dynamical system. The efficacy and robustness of the controller vis a vis unknown but bounded disturbances and state measurement errors is investigated analytically and numerically. As an example of a dynamical system we consider a single degree of freedom mass—spring—damper system that is excited by an unknown force. The control scheme presupposes that the spring and damping coefficients can be varied within prescribed bounds, albeit not independently. The construction of such a semiactive controller can be realized by using the properties of so calledelectrorheological fluids (see [1] for relevant experimental investigations). The called for changes in spring and damping properties can be effected in microseconds since the control does not involve the separate dynamics (inertia) of usual actuators. The design of the controller is based on Lyapunov stability theory which is also utilized to investigate the stabilizing properties of the controller. To accommodate state measurement errors the proposed control scheme is combined with afuzzy control concept. Simulations are carried out for examples of periodic, continuous nonperiodic, discontinuous periodic and random excitation forces.

Comparison of the aerodynamic forces on a flying sphingid moth with those predicted by quasi-steady theory

Abstract: A camera and strain-gauge probe were used to record the wing beat and instantaneous vertical and horizontal forces on a sphingid moth flying in a wind of 336 m s⁻¹ The data were averaged over several wing beats to remove beat-to-beat variation The moth was producing suffcient upward force to balance its weight of 147 mN and approximately sufficient thrust to balance its drag The film of the wing beat was used to predict the wing inertial and virtual mass forces The experimental aerodynamic force was obtained by subtracting the inertial force from the recorded force The film was also used to predict the quasisteady aerodynamic forces due to wing translation and rotation The vertical experimental aerodynamic and total predicted (quasi-steady plus virtual mass) forces have a similar shape, but the experimental downstroke peak (70 mN) was larger than predicted (47 mN) The horizontal recorded forces are smaller than the vertical forces, and wing inertia is a large component However, a small aerodynam

Vibratory angular rate sensor

Abstract: A single-axis angular rate sensor is comprised of a transducer and associated electronics. The transducer consists of a symmetric planar inertia member supported by symmetrically disposed coplanar elastic beams. The inertia member is angularly oscillated about its center of gravity about a first axis. Rotation of the sensor about a third orthogonal axis results in Coriolis moments, causing angular oscillations about an orthogonal second axis. The angular oscillations about the second axis are restrained by means of voltages applied to electrostatic electrodes. These voltages are proportional to the angular input rate.

On the motion of small spherical bubbles in two‐dimensional vortical flows

Abstract: The motion of small, spherical noninteracting bubbles in two‐dimensional vortical flows by means of numerical simulations is investigated. After a discussion concerning the various bubble equations, bubble trajectories are calculated in a solid‐body vortex, where it is found that the bubble motion can be described in terms of the location where the bubbles accumulate, or equilibrium points, and the rate of entrapment into these equilibrium points. Of importance here is that the rate of entrapment into the vortex has an optimum value for some value of the inertia parameter, or inverse Stokes number. The bubble motion in a temporally evolving shear layer is investigated, where it is found that the solid‐body vortex model predicts the trends in the growth in concentration about the vortex center for the case without gravity. For the case with gravity, not all bubbles are captured by the vortex, and the percentage of bubbles captured increases with decreasing inertia parameter. Also discussed is how these factors affect the generation of the interface between regions seeded and not seeded with bubbles.

Dynamic response of a beam on elastic foundation of finite depth under a moving force

Abstract: In this paper, dynamic response of an infinitely long beam resting on a foundation of finite depth, under a moving force is studied. The effect of foundation inertia is included in the analysis by modelling the foundation as a series of closely spaced axially vibrating rods of finite depth, fixed at the bottom and connected to the beam at the top. Viscous damping in the beam and foundation is included in the analysis. Steady state response of the beam-foundation system is obtained. Detailed numerical results are presented to study the effect of various parameters such as foundation mass, velocity of the moving load, damping and axial force on the beam. It is shown that foundation inertia can considerably reduce the critical velocity and can also amplify the beam response.

The motion of an elliptical cylinder in channel flow at low Reynolds numbers

Abstract: The motion of an elliptical cylindrical particle immersed in an incompressible Newtonian fluid in a narrow channel is examined numerically in the zero-Reynolds-number limit. It is assumed that no external forces or torques act on the elliptical cylinder, and the effects of inertia forces on the motion of the fluid and the particle are neglected. The Stokes equations are solved by a finite-element method for various positions and orientations of the cylinder, yielding the instantaneous velocities of the particle that satisfy the conditions of zero force and zero torque on the particle. Using the computed longitudinal, lateral, and angular velocities of the particle, the evolution of the particle's position and orientation is determined for various initial configurations. An elliptical cylinder is found to either tumble or oscillate in rotation, depending on the particle-channel size ratio, the axis ratio of the elliptical cylinder, and the initial conditions. In the first case, the particle rotates continuously in one direction that is well approximated by Jeffery's solution for an elliptical cylinder in unbounded shear flow with a so-called equivalent axis ratio; in the second case, the particle changes its direction of rotation during part of each period. In both cases, the particle translates with a periodically varying longitudinal velocity, accompanied by a considerable side drift due to the walls. The oscillatory motion is more likely to occur when the particle-channel size ratio or axis ratio is increased. The tumbling motion is inhibited for elliptic cylinders whose size ratios are larger than threshold values that depend on the axis ratio.

Visualization of the Flows in Precessing Tanks with Internal Baffles

Abstract: This paper presents an experimental investigation of some fluid flows inside a precessing right circular cylindrical tank. The first aim was to determine the extent to which a wave modal description of the fluid flow, which is physically realizable for a tank with no internal baffles, is sustained when the geometry of the tank is modified by baffle plates. The second was to determine if a baffle plate configuration could be found that forestalled the development of low-order modes. This second aim is directed toward the goal of eliminating low-order mode resonances in the fuel tanks of spinning spacecraft. Instabilities of such spacecraft have been successfully minimized at the design stage by the incorporation of baffle plates optimized by empirical "drop tests." The ability of a baffle plate to eliminate low-order resonances, provided it is of a particular optimal configuration, is confirmed in this paper. This result suggests the use of flow visualizations as a means of simplifying expensive empirical drop-test programs. I. Introduction I N recent years, increasing proportions of the masses of spacecraft have been made up of fluids. These are the liquid fuels required to make small corrections to the orbits of communications satellites that are becoming more complex and must stay in operation for longer times. Spinning interplanetary probes must also carry more liquid fuels to execute increasingly complex missions. The stability of such spacecraft must be insured at the design stage. A rigid spacecraft will spin stably about either its axis of least inertia or its axis of greatest inertia. However, if energy is dissipated when a spacecraft is spinning about its axis of least inertia (a common configuration for a satellite in geostationary transfer orbit), this configuration is unstable. The spacecraft's nutation angle diverges as it tends to a spin about its axis of greatest inertia, this being the state of lowest energy for a given angular momentum. In a spacecraft containing liquid fuels, "dissipation" can include the transfer of energy from the rigid spacecraft's motion to the fluid. The fluid motion could occur on a variety of spatial scales, ranging from the large (low wave number waves) to the small (turbulence). In addition, viscous friction causes energy losses in boundary or shear layers. Drop-test experiments1 were carried out on scaled models of the Eurostar spacecraft bus. The internal liquid-containing tanks in both the models and the prototype spacecraft were right circular cylinders with hemispherical ends. In a drop-test experiment, a scale model of the spacecraft and its contained fluids is spun up at the top of a shaft. The model is dropped and briefly experiences free fall. During its fall, the model's overall angular velocity is recorded so that the prototype's stability in orbit may be inferred. Exponential growth of the nutation angle 0 of the spinning model was reported; the model was unstable. The nutation angle diverged according to 0

Formulation and solution of inverse spaghetti problem - Application to beam deployment dynamics

Abstract: A finite element model of the dynamics of axially moving, highly flexible beams is presented. The model is based on a geometrically nonlinear beam formulation that allows for large overall motions. To account for the varying length of a deploying beam, a moving finite element reference grid is incorporated within the nonlinear beam formulation such that the number of finite element nodes remains fixed and the finite element length is allowed to vary. Hamilton's law is used to formulate the equations of motion, and a transient integration solution procedure is derived from a space-time finite element discretization of the Hamiltonian variational principle. Computational results of the methodology are presented for a planar inverse-spaghetti problem. HE dynamics of axially moving beamlike structures are becoming increasingly important for the analysis of spacecraft and large space structures that deploy flexible appendages such as antenna, stabilizing booms, solar arrays, and long trusslike structures as well as for other applications such as magnetic tape drives, printing machines, traveling cables, and band saws. An extensive amount of research has focused on the modeling of axially moving continua to analyze the dynamic behavior of such structures. One of the most common models of axially moving continua that has received the most attention is the traveling string problem. In what he termed the "spaghetti problem," Carrier1 analyzed the motion of a string being accelerated upward into a fixed orifice. In other works since then, analytical expressions representing both linear and nonlinear vibrations of axially moving strings subject to various support conditions have been derived.2'9 The dynamics of beamlike structures traveling between or over fixed supports have also been studied to address industrial applications such as high-speed tape drives and band saws.10'13 To address spacecraft applications in which antenna or other long flexible structures are deployed from a host satellite, the dynamics of a cantilever beam that is ejected from a single fixed guide are modeled using Bernoulli-Euler beam theory in Ref. 14. In a quite different approach, the extrusion of a beam from a rotating base is modeled using a series of elastically connected rigid links in which the number of rigid links are continuously increased/decreased to account for deployment/ retrieval of the beam.15 General formulations of axially moving Bernoulli-Euler beam models cantilevered to a rotating rigid host body have also been developed to study the effect of appendage deployment on the attitude dynamics of orbiting spacecraft.16"20 All of these given analyses are based on an assumption of small elastic deformations. With the exception of the discrete spring-mass model of Ref. 15, all of the other models that have been referenced thus far use linear combinations of space-depende nt admissible functions of a time-varying length weighted by time-dependen t generalized coordi

Observations on the Nonlinear Fluid Forces in Short Cylindrical Squeeze Film Dampers

Abstract: Recent theoretical work by Tichy and Bou-Said (1991) and El-Shafei and Crandall (1991) has resulted in new theoretical expressions for the nonlinear inertia forces for both short and long cylindrical squeeze film dampers (SFDs). This paper provides alternative derivations for the short cylindrical SFD using as a starting point a simplified two-dimensional Navier-Stokes equation. The resulting expressions for the fluid inertia forces are similar to the Tichy and Bou-Said/El-Shafei and Crandall expressions except for differences in certain numerical constants which can be explained by the different averaging methods used within the squeeze-film thickness. The analyses give additional insight into the temporal and convective origins of the various coefficients. The theoretical results are compared with published theoretical and experimental work involving nonlinear cylindrical SFD behavior. The paper highlights the importance of convective inertia terms when cylindrical SFDs operate at large values of eccentricity ratio.

Approximate Analysis of Flexible Parts in Multibody Systems Using the Finite Element Method

Abstract: An easy applicable procedure for the approximate analysis of a flexible body in a multibody system (MBS) is presented. It is based on the major assumptions that the elastic deformations in the MBS are small and that their effect upon the large motion of the MBS is negligible. It can be carried out using a standard code for the analysis of rigid multibody systems and a nonlinear general purpose finite element program which has to be extended, so that the inertia forces and the constraint forces acting on the examined body can be applied. Deformations and stresses are calculated for some examples, also including the effects of dynamic coupling and dynamic stiffening as well as contact problems.

Inertia of Casimir energy

Abstract: Moving mirrors are submitted to reaction forces by vacuum fields. The motional force is known to vanish for a single mirror uniformly accelerating in vacuum. We show that inertial forces (proportional to accelerations) arise in the presence of a second scatterer, exhibiting properties expected for a relative inertia: the mass corrections depend upon the distance between the mirrors, and each mirror experiences a force proportional to the acceleration of the other one. When the two mirrors move with the same acceleration, the mass correction obtained for the cavity represents the contribution to inertia of Casimir energy. Accounting for the fact that the cavity moves as a stressed rigid body, it turns out that this contribution fits Einstein's law of inertia of energy.