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Showing papers on "Angular velocity published in 1996"


Journal ArticleDOI
TL;DR: This note shows that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement, and exploits the inherent passivity of the system.
Abstract: It is well known that the linear feedback of the quaternion of the attitude error and the angular velocity globally stabilizes the attitude of a rigid body. In this note, we show that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement. In contrast to other approaches, this design exploits the inherent passivity of the system; a model-based observer reconstructing the velocity is not needed. An application of the proposed scheme is illustrated for the robot control problem. Simulation results are included to illustrate the theoretical results.

397 citations


Journal ArticleDOI
TL;DR: In this paper, the axial trapping forces within optical tweezers arising from Laguerre-Gaussian laser modes were numerically modeled for an 8 μm diameter sphere suspended in water.
Abstract: We numerically model the axial trapping forces within optical tweezers arising from Laguerre–Gaussian laser modes. For an 8 μm diameter sphere suspended in water, the higher-order modes produce an axial trapping force several times larger than that of the fundamental. Partial absorption results in a transfer of the orbital angular momentum from the Laguerre–Gaussian mode to the trapped particle. This results in the rotation of the particle by what may be called an optical spanner (wrench). For an absorption coefficient of α = 5700 m−1 and a laser power of 10 mW, we find that an 8 μm diameter sphere would acquire an angular acceleration of 10 × 104 rad s−2 and a limiting angular velocity of 0.2 rad s−1.

257 citations


Journal ArticleDOI
TL;DR: In this paper, a novel approach for pumping fluids in micromechanical applications at extremely low Reynolds numbers is presented, based on the rotation of a cylinder placed asymmetrically in a narrow duct; the differential viscous resistance between the small and large gaps causes a netflow along the channel.
Abstract: Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre Dame, IN 46556We present a novel approach for pumping fluids in micromechanical applications atextremely low Reynolds numbers. It is based on the rotation of a cylinder placed asymmetricallyin a narrow duct; the differential viscous resistance between the small and large gaps causes a netflow along the channel. We report on experiments using glycerin and several cm-scale prismshaving circular, square and rectangular cross-sections. The Reynolds number, based on cylindersize and angular velocity, varies in the range of 0.01–10. The flow is visualized using tracerparticles. The flow generated depends on the geometrical parameters, but is proportional to theangular velocity of the cylinder. An average flow velocity that is about 10% of the surface speedof the cylinder has been obtained.Manufacturing processes that can create extremely small machines have been developed inrecent years. Motors, electrostatic actuators, pneumatic actuators, valves, gears and tweezers ofabout 10 µm size have been fabricated. These have been used as sensors for pressure,temperature, velocity, mass flow, or sound, and as actuators for linear and angular motions.Current usage ranges from airbags to blood analysis (O'Connor, 1992). There is considerablework under way to include other applications, one example being the micro-steam engine describedby Lipkin (1993). Many of these new applications will need fluid to be pumped in a duct; at suchsmall scales this is a challenge.There have been several studies of microfabricated pumps. Some of them use non-mechanical effects. Ion-drag is used in electrohydrodynamic pumps (Bart et al., 1990; Richter et

123 citations


Journal ArticleDOI
TL;DR: Traffic flow models that include human visual characteristics must consider the "dead zones" in response produced by thresholds of subtended angle change subtended angular velocity and the non-linear relationship between perceived relative velocity and actual relative velocity.

116 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that the acceleration of a point in the end effector of a serial chain can be expressed in terms of the direction and moment parts of the same screw coordinates.

102 citations


Journal ArticleDOI
TL;DR: The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997) by direct operation on the data as mentioned in this paper.
Abstract: The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997). Rather than fit the data to a family of models, we generate estimates of all dynamical functions nonparametrically, by direct operation on the data. The cluster is assumed to be oblate and edge-on but mass is not assumed to follow light. The mean motions are consistent with axisymmetry but the rotation is not cylindrical. The peak rotational velocity is 7.9 km/s at 11 pc from the center. The apparent rotation of Omega Centauri is attributable in part to its proper motion. We reconstruct the stellar velocity ellipsoid as a function of position, assuming isotropy in the meridional plane. We find no significant evidence for a difference between the velocity dispersions parallel and perpendicular to the meridional plane. The mass distribution inferred from the kinematics is slightly more extended than, though not strongly inconsistent with, the luminosity distribution. We also derive the two-integral distribution function f(E,Lz) implied by the velocity data.

85 citations


Journal ArticleDOI
01 Sep 1996
TL;DR: The results suggest that in practical kinesiological applications, adding either an accelerometer or an angular rate sensor can remarkably increase the accuracy of segmental COM acceleration estimates.
Abstract: A system based on the integrated kinematic sensor (IKS) was used to study the three-dimensional (3-D) kinematics of human lower limb during walking and running. The linear displacement, angular velocity, and linear acceleration of the foot, shank, and thigh segments were directly measured using three IKSs. The results clearly showed the heel strike impact in both walking and running, illustrating the high frequency components that exist in those activities. This paper illustrates the limitations of standard position measurements to capture transients associated with phase transitions, not only in acceleration estimates, but also in the determination of segmental angular velocities. An error analysis was conducted to determine the relative contribution of the accelerometer and the angular rate sensor to the determination of the segmental center of mass (COM) acceleration. The results suggest that in practical kinesiological applications, adding either an accelerometer or an angular rate sensor can remarkably increase the accuracy of segmental COM-acceleration estimates.

80 citations


Journal ArticleDOI
TL;DR: The results of this study show that the primate low-frequency enhancement of VOR dynamics during off-vertical axis rotation is independent of a simultaneous activation of the vertical and torsional "tilt" otolith-ocular reflexes that have been characterized in the preceding paper.
Abstract: 1. The dynamic contribution of otolith signals to three-dimensional angular vestibuloocular reflex (VOR) was studied during off-vertical axis rotations in rhesus monkeys. In an attempt to separate response components to head velocity from those to head position relative to gravity during low-frequency sinusoidal oscillations, large oscillation amplitudes were chosen such that peak-to-peak head displacements exceeded 360 degrees. Because the waveforms of head position and velocity differed in shape and frequency content, the particular head position and angular velocity sensitivity of otolith-ocular responses could be independently assessed. 2. During both constant velocity rotation and low-frequency sinusoidal oscillations, the otolith system generated two different types of oculomotor responses: 1) modulation of three-dimensional eye position and/or eye velocity as a function of head position relative to gravity, as presented in the preceding paper, and 2) slow-phase eye velocity as a function of head angular velocity. These two types of otolith-ocular responses have been analyzed separately. In this paper we focus on the angular velocity responses of the otolith system. 3. During constant velocity off-vertical axis rotations, a steady-state nystagmus was elicited that was maintained throughout rotation. During low-frequency sinusoidal off-vertical axis oscillations, dynamic otolith stimulation resulted primarily in a reduction of phase leads that characterize low-frequency VOR during earth-vertical axis rotations. Both of these effects are the result of an internally generated head angular velocity signal of otolithic origin that is coupled through a low-pass filter to the VOR. No change in either VOR gain or phase was observed at stimulus frequencies larger than 0.1 Hz. 4. The dynamic otolith contribution to low-frequency angular VOR exhibited three-dimensional response characteristics with some quantitative differences in the different response components. For horizontal VOR, the amplitude of the steady-state slow-phase velocity during constant velocity rotation and the reduction of phase leads during sinusoidal oscillation were relatively independent of tilt angle (for angles larger than approximately 10 degrees). For vertical and torsional VOR, the amplitude of steady-state slow-phase eye velocity during constant velocity rotation increased, and the phase leads during sinusoidal oscillation decreased with increasing tilt angle. The largest steady-state response amplitudes and smallest phase leads were observed during vertical/torsional VOR about an earth-horizontal axis. 5. The dynamic range of otolith-borne head angular velocity information in the VOR was limited to velocities up to approximately 110 degrees/s. Higher head velocities resulted in saturation and a decrease in the amplitude of the steady-state response components during constant velocity rotation and in increased phase leads during sinusoidal oscillations. 6. The response characteristics of otolith-borne angular VORs were also studied in animals after selective semicircular canal inactivation. Otolith angular VORs exhibited clear low-pass filtered properties with a corner frequency of approximately 0.05-0.1 Hz. Vectorial summation of canal VOR alone (elicited during earth-vertical axis rotations) and otolith VOR alone (elicited during off-vertical axis oscillations after semicircular canal inactivation) could not predict VOR gain and phase during off-vertical axis rotations in intact animals. This suggests a more complex interaction of semicircular canal and otolith signals. 7. The results of this study show that the primate low-frequency enhancement of VOR dynamics during off-vertical axis rotation is independent of a simultaneous activation of the vertical and torsional "tilt" otolith-ocular reflexes that have been characterized in the preceding paper. (ABSTRACT TRUNCATED).

77 citations


Patent
21 Jun 1996
TL;DR: In this article, an angular velocity sensor using vibration of a piezoelectric oscillation piece has the first axis for detecting the angular velocity and the second axis set along a direction orthogonal to the first one, and a detection sensitivity is 15-55% of detection sensitivity of the first.
Abstract: PROBLEM TO BE SOLVED: To provide an angular velocity sensor capable of detecting precisely an angular velocity, even when an angle of a detection axis of the angular velocity sensor to an actual rotation applied axis is great, without inclining a piezoelectric oscillator to be fixed. SOLUTION: This angular velocity sensor using vibration of a piezoelectric oscillation piece has the first axis for detecting the angular velocity and the second axis set along a direction orthogonal to the first axis, and a detection sensitivity of the second axis is 15-55% of detection sensitivity of the first axis. Sensitivity correction of 15% or less is enough in attaching wherein an angle of the detection axis of the angular velocity sensor to the actual rotation applied axis is up to 40°, and an output sensitivity caused by the attaching angle can be corrected by computation processing based on a software. COPYRIGHT: (C)2008,JPO&INPIT

75 citations



Proceedings ArticleDOI
06 Oct 1996
TL;DR: A new high performance sensorless speed vector controller that implements the maximum torque per ampere control strategy for the inverter driven synchronous reluctance machine is presented in this paper, based on a parameter dependent technique for on-line estimation of rotor position and angular velocity at the control rate.
Abstract: A new high performance sensorless speed vector controller that implements the maximum torque per ampere control strategy for the inverter driven synchronous reluctance machine is presented in this paper. It is based on a parameter dependent technique for on-line estimation of rotor position and angular velocity at the control rate. The current ripple principle is used to estimate position. The estimates are fed to a conventional closed-loop observer to predict the new position and angular velocity. The very high accuracy of the sensorless control algorithm at both low and high speeds is confirmed by experimental results.

Patent
Satoshi Usa1
06 May 1996
TL;DR: In this paper, the gyro sensors are employed to accurately detect hand-swing motion applied to the hand controller without being affected by gravity, and a peak detection process is performed on the angular velocity to determine a beat timing designated by the human operator.
Abstract: An automatic performance control apparatus provides a hand controller which contains gyro sensors in X, Y directions. The gyro sensors are employed to accurately detect hand-swing motion applied to the hand controller without being affected by gravity. When the hand controller is swung by a human operator like a conductor's baton, angular velocity applied to the hand controller is detected based on detection values of the gyro sensors. The angular velocity becomes bottom at a change point of direction in a locus of the hand-swing motion of the hand controller; and a peak of the angular velocity appears between bottoms. So, peak detection process is performed on the angular velocity to determine a beat timing designated by the human operator. If the peak is detected, beat-timing detection data are automatically created and are transmitted to an electronic musical instrument having an automatic performance function. Based on the beat-timing detection data, the electronic musical instrument performs tempo control during progression of automatic performance in real time. Moreover, beat-number determination process is performed to make a decision as to which of beats in triple time corresponds to a current peak of the angular velocity. The tempo control of the automatic performance responds to a beat number determined, thus avoiding a deviation between beats of the automatic performance and beats designated by he human operator. Incidentally, it is possible to further provide acceleration sensors which cooperate with the gyro sensors to assist the peak detection.

Journal ArticleDOI
TL;DR: A Feedback control law is presented that gives exponential convergence of a nonholonomic underwater vehicle to a constant desired configuration using a piecewise smooth feedback control law that is based on previous work on the control of non holonomic mobile robots in the plane.
Abstract: In this article we present a feedback control law that gives exponential convergence of a nonholonomic underwater vehicle to a constant desired configuration. This is achieved using a piecewise smooth feedback control law that is based on previous work on the control of nonholonomic mobile robots in the plane. The kinematic model of the underwater vehicle is given in SE(3) by homogeneous transformation matrices, and attitude deviations are given by Euler parameters. This gives a global description without singularities. It is also shown how controllability of the nonholonomic underwater vehicle can be analyzed in SE(3) without the use of local charts. The inputs of the system are the three angular velocity components and the forward velocity.

Patent
17 Oct 1996
TL;DR: In this article, the angular velocities of the vehicle about the yaw axis (z'), the rolling axis (x') and the pitch axis (y') are measured in a vehicle using rotation-rate sensors (DSx, DSy, DSz).
Abstract: To detect roll-overs reliably and in good time, the angular velocities of the vehicle (FZ) about the yaw axis (z'), the rolling axis (x') and the pitch axis (y') are measured in a vehicle using rotation-rate sensors (DSx, DSy, DSz). An angular velocity exceeding a predetermined threshold indicates that a roll-over has been detected.

Journal ArticleDOI
TL;DR: In this paper, a mechanism is proposed to explain the seismologically-inferred prograde rotation of the Earth's solid inner core in terms of the structure of convection in the fluid outer core.
Abstract: A mechanism is proposed to explain the seismologically-inferred prograde rotation of the Earth's solid inner core in terms of the structure of convection in the fluid outer core. Numerical calculations of convection and dynamo action in the outer core exhibit excess temperatures inside the tangent cylinder surrounding the inner core. We show that this temperature difference generates a prograde thermal wind and a strong azimuthal magnetic field inside the tangent cylinder. Electromagnetic torques on the inner core derived from induced azimuthal magnetic fields and the ambient poloidal field equilibrate when the inner core angular velocity lags the nearby tangent cylinder fluid angular velocity by approximately 14%. The inferred prograde rotation of the inner core (1.1–3°/year relative to the mantle) can be produced by a very small (⋍ 0.001 K) temperature anomaly within the tangent cylinder and indicates strong toroidal magnetic fields with peak intensities of 24–66 mT in that region of the core.

Journal ArticleDOI
TL;DR: In this article, the Coriolis force and the low Reynolds number of a two-dimensional turbulent channel were analyzed and the relevant parameters of this flow were found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and D/u* for the core region.
Abstract: Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2Um D/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.

Patent
02 Apr 1996
TL;DR: In this paper, the target is captured by an array antenna 10 by executing first search control immediately after a power source is applied after the target was captured, tracking control by a beam switch control part 46 for azimuth is performed The output of an angular velocity sensor 20 is affected on a tracking signal after it is filtered by a high-pass filter 48 Angular velocity around the azIMuth axis 32 of the array antenna can be kept at zero even in a state in which no signal is received from the target.
Abstract: PURPOSE: To track a target by utilizing sensor output CONSTITUTION: The target is captured by an array antenna 10 by executing first search control immediately after a power source is applied After the target is captured, tracking control by a beam switch control part 46 for azimuth is performed The output of an angular velocity sensor 20 is affected on a tracking signal after it is filtered by a high-pass filter 48 Angular velocity around the azimuth axis 32 of the array antenna 10 can be kept at zero even in a state in which no signal is received from the target Even in the case that the signal from the target can be received, a control system can be stabilized by feeding back such angular velocity

Journal ArticleDOI
TL;DR: In 3 experiments, observers witnessed a target moving along a circular orbit and indicated the location at which the target vanished, and displacement patterns were consistent with hypotheses that analogues of momentum and centripetal force were incorporated into the representational system.
Abstract: In 3 experiments, observers witnessed a target moving along a circular orbit and indicated the location at which the target vanished. The judged vanishing point was displaced forward in the direction of implied momentum and inward in the direction of implied centripetal force. In general, increases in either the angular velocity of the target or the radius length of the orbit increased the magnitude of forward displacement. If both angular velocity and radius length were varied, then increases in either angular velocity or radius length also increased the magnitude of inward displacement. The displacement patterns were consistent with hypotheses that analogues of momentum and centripetal force were incorporated into the representational system. A framework is proposed that accounts for (a) the forward and inward displacements and (b) naive-physics data on the spiral tube problem previously interpreted as suggesting a belief in a naive curvilinear-impetus principle.

Patent
18 Dec 1996
TL;DR: In this article, a position tracker uses an inertial angular measurement system, for measuring orientation and linear translation of a helmet on a human head for the synthesis by a host computer of virtual, directional audio over headphones sensors mounted on the helmut.
Abstract: A position tracker uses an inertial angular measurement system, for measuring orientation and linear translation of a helmet on a human head for the synthesis by a host computer of virtual, directional audio over headphones sensors mounted on the helmut, includes a roll gyro sensor, a pitch gyro sensor, a yaw gyro sensor, an absolute roll tilt sensor coupled to a first universal signal conditioner, an absolute pitch tilt sensor coupled to a second universal signal conditioner, and an absolute yaw compensator. A data acquisition system is coupled between the sensors and the host computer for converting analog signals from the sensors into digital, angular orientation data. Each of the gyro sensors includes angular velocity detectors and solid state electronic devices connected to provide angular velocity signals at a given sample rate.

Journal ArticleDOI
TL;DR: In this article, a nonlinear event-based observer is proposed to estimate the unknown system input, that is, the indicated torque, from one or more measurements of crankshaft angular velocity.

Journal ArticleDOI
TL;DR: It is concluded that the centrifugal force, measured by otoliths and truncal graviceptors, serves to provide information on angular velocity at eccentric rotation, at least as long as the output of the velocity storage is not yet zero.
Abstract: In three psychophysical experiments subjects (Ss), blindfolded and earphoned with white noise, estimated their angular speed A) after brief acceleration to constant centric or eccentric rotation, and B) after deceleration to a full stop. Ss either indicated whenever they were rotated through 180 degrees, or manipulated the objective velocity such that the subjective one stayed constant. With Ss in an earth-vertical attitude, subjective speed declined exponentially with a time constant that depended on eccentricity in paradigm A, but not in B. The time constant depended linearly on the amount of the centrifugal force, but not on its direction. Thus, centrifugal force has an enhancing effect on perceived angular speed. The relevant sense organs were identified with Ss in a radial, earth-horizontal attitude. The enhancing effect was minimal when the axis of rotation was caudal of the otoliths, indicating an effect of graviceptors in the trunk. This effect, just as the effect of recently discovered truncal graviceptors on the perception of posture, turned out to depend on leg position: The minimum of the enhancing effect shifted from about 30 cm to about 60 cm caudal of the otoliths, when leg position changed from flexed to extended. It is concluded that the centrifugal force, measured by otoliths and truncal graviceptors, serves to provide information on angular velocity at eccentric rotation, at least as long as the output of the velocity storage is not yet zero.

Journal Article
TL;DR: Three-dimensional displacement histories of 16 selected landmarks were calculated using the direct linear transformation approach and 3-D individual segment rotations for the upper limb were Calculated using vector equations to identify modifications to stroke technique from those previously identified in the flat forehand drive.
Abstract: Increased topspin in the tennis forehand is produced by maintaining a perpendicular racket-face to the court surface at impact and increasing the trajectory and vertical velocity of the racket-head. These modifications to stroke technique from those previously identified in the flat forehand drive are the result of changes to the movement patterns of the segments of the upper limb. The contributions that the upper limb segment's anatomical rotations make to racket-head velocity at impact depend on both their angular velocity and the instantaneous position of the racket with respect to these movements. Six high performance tennis players were filmed at a nominal rate of 200 Hz by three Photosonics cameras while hitting flat (no spin) and topspin groundstrokes and a forehand topspin lob. The three-dimensional (3-D) displacement histories of 16 selected landmarks were then calculated using the direct linear transformation approach and 3-D individual segment rotations for the upper limb were calculated using vector equations. Significant differences were recorded in the effect that the various segment rotations made to the x-direction (forward) and y-direction (upward) impact velocities of the racket-head. These differences were not reflected in the contributions to racket-head velocity when the absolute velocities were expressed relative to the impact velocity. Trunk rotation, upper arm flexion/abduction, upper arm internal rotation, hand palmar and ulnar flexion all played integral roles in producing impact racket speed.

Patent
08 Nov 1996
TL;DR: In this article, a travel-situation-dependent steering angle is derived as a function of the actual value of the yaw angular velocity as well as the predetermined characteristic value.
Abstract: A process is provided for determining a travel-situation-dependent steering angle, in which a specification of a characteristic value for the transverse motion of the vehicle is given, the actual value of the yaw angular velocity of the vehicle is evaluated, and a criterion is derived as a function of the actual value of the yaw angular velocity as well as the predetermined characteristic value. As a function of the criterion, an influencing of the travel behavior of the vehicle takes place by an intervention in the vehicle steering. For the derivation of the criterion, additionally the side slip angle, the steering angle and the vehicle velocity are evaluated, and, for the derivation of the criterion, the lateral forces at the vehicle wheels are taken into consideration.

Patent
04 Nov 1996
TL;DR: An optical velocity measuring device includes a pair of V/H sensors effectively located at two different distances from a moving object, each sensor is used to determine an image velocity and a corresponding angular velocity of the object as discussed by the authors.
Abstract: An optical velocity measuring device includes a pair of V/H sensors effectively located at two different distances from a moving object. Each sensor is used to determine an image velocity and a corresponding angular velocity of the object. The angular velocity measurements and the difference in distance or optical path length of the individual sensors are used to determine the absolute linear tangential speed of the object without determining the absolute distance to the object.

Patent
10 Jul 1996
TL;DR: In this article, an angular velocity sensor for detecting angular velocity components about three axes with high response is provided, where a weight body carries out a circular movement along a circular orbit within the XY-plane with the origin being as a center.
Abstract: An angular velocity sensor for detecting angular velocity components about three axes with high response is provided. A weight body carries out a circular movement along a circular orbit within the XY-plane with the origin being as a center. The weight body is supported so that it can be moved with a predetermined degree of freedom within a sensor casing. A Coriolis force Fco exerted in the Z-axis direction to the weight body is detected when the weight body passes through the X-axis at the point Px and an angular velocity ωx about the X-axis is obtained based on the detected force. Further, a Coriolis force Fco exerted in the Z-axis direction to the weight body is detected when the weight body passes through the Y-axis at the point Py and an angular velocity ωy about the Y-axis is obtained based on the detected force. In addition, a force exerted in the X-axis direction to the weight body at the point Px is detected and an angular velocity ωz about the Z-axis is obtained based on the detected force by eliminating a centrifugal force.

Journal ArticleDOI
TL;DR: In this paper, the dynamics of a fast rotating symmetric rigid body in an arbitrary analytic potential, by means of the techniques of Hamiltonian perturbation theory, specifically Nekhoroshev's theory, was studied.
Abstract: In this paper we study the dynamics of a fast rotating symmetric rigid body in an arbitrary analytic potential, by means of the techniques of Hamiltonian perturbation theory, specifically Nekhoroshev's theory. For a rigid body with a fixed point, this approach allows us to get an accurate description of the motion (with rigorous estimates) on time scales which increase very fast with the angular velocity of the body, precisely as . As we show, on such time scales, the body performs an approximately free motion around the instantaneous direction of the angular momentum vector m, which in turn moves slowly in space, with speed of order . The properties of such a slow drift of m strongly depend on the resonance properties of the initial angular velocity. For nonresonant initial conditions, the unit vector in the direction of m closely follows, on the unit sphere, the level curves of an averaged external potential, so the motion is essentially regular (chaotic effects, if any, are confined to small-amplitude oscillations around such motion). On the contrary, in case of resonance, can perform large-scale chaotic motions, which spread over genuinely two-dimensional regions of the unit sphere; numerical evidence of this phenomenon in an oversimplified model is also provided. Similar results are proven for prolate rigid bodies with no fixed point; an important difference is that, because of the presence of additional `slow' degrees of freedom, a large-scale chaotic behaviour of m is now possible in nonresonant motions, too. Because of the presence of singularities of the action-angle coordinates, our description is not optimal for motions very close to gyroscopic rotations; the forthcoming part II will be devoted to these special motions.

Journal ArticleDOI
TL;DR: It is shown here that most controls proposed in the past are not robust with respect to errors in the location of the actuators, and robust asymptotically stabilising feedbacks are derived.

Journal ArticleDOI
TL;DR: In this paper, a linearization of second-order strain-displacement equations for elastic bodies is proposed to obtain the governing dynamical equations of a rigid body undergoing high angular velocity, and the analysis is illustrated by a series of examples of variously configured rotating beams and plates.
Abstract: This paper presents an analysis of the dynamics of flexible bodies undergoing high angular velocity. It is shown that the high angular velocity produces a stiffening of the body, which can easily be neglected by an untimely, or inconsistent, linearization of the dynamical equations. The analysis presented is based on a linearization of second-order strain-displacement equations for elastic bodies. Kane's equations are then used to obtain the governing dynamical equations. It is asserted that this procedure produces a consistent linearization of the governing equations and, in the process, captures so-called “dynamic stiffening” terms that are sometimes lost with inconsistent linearizations. The analysis is illustrated by a series of examples of variously configured rotating beams and plates. In addition to deformations, the analysis is also used to compute restraint forces at the structural supports. It is seen that some of these forces can easily be missed with inconsistent linearization of the ...

Patent
20 Nov 1996
TL;DR: In this paper, a position and speed sensor comprising a circular element (1) rotatably driven about its axis is presented, and an electrical signal is produced by the sensor means (5) corresponding to the passage of each of the sensed position indicators (3, 4).
Abstract: A position and speed sensor comprising a circular element (1) rotatably driven about its axis. The circular element (1) has two position indicators (3, 4) of different angular width. A sensor means (5) is fixed in position with respect to and adjacent to the circular element (1). The sensor means (5) has a sensing element for sensing the passage of each of the position indicators (3, 4) past the sensing element. An electrical signal is produced by the sensor means (5) corresponding to the passage of each of the sensed position indicators (3, 4). The signal has a duration corresponding to the angular widths of the sensed position indicators (3, 4). Also included is a means to process the electrical signal to produce information as to the angular position and angular velocity of the circular element. A method for reverse rotation detection using the position and speed sensor means (5) is also disclosed.

Patent
Tsuyoshi Morofuji1
27 Feb 1996
TL;DR: In this paper, a variable angle prism (VAP) is driven on the basis of the vibration signal, the offsets of the frequency characteristic, the driving limit and the initial position are detected from the response characteristics obtained when a predetermined test driving signal is supplied to the VAP, and the offsets are corrected.
Abstract: It is an object of the present invention to obtain optimum driving characteristics by correcting a deterioration in vibration correction characteristics, which is caused by a mechanical degradation such as shaft friction or deformation caused by the temperature and time change of vibration correction unit, or variations caused by the difference between individual devices. In order to achieve this object, a vibration correction apparatus for correcting the movement of an image which is caused by a vibration includes a calibration function by which an angular velocity detected by an angular velocity detection unit is integrated and converted into an angular displacement signal to generate a vibration signal, a variable angle prism (VAP) is driven on the basis of the vibration signal, the offsets of the frequency characteristic, the driving limit, and the initial position are detected from the response characteristics obtained when a predetermined test driving signal is supplied to the VAP, and the offsets are corrected.