Determination Of Angular Velocity Research Articles

GNSS gyroscopes: determination of angular velocity and acceleration with very high-rate GNSS

Although global navigation satellite systems (GNSS) have been routinely applied to determine attitudes, there exists no literature on determining angular velocity and/or angular acceleration from GNSS. Motivated by the invention of computerized accelerometers of the correspondence author and following the success of accurately recovering translational velocity and acceleration waveforms from very high-rate GNSS precise positioning by Xu and his collaborators in 2021, we propose the concept of GNSS gyroscopes and reconstruct angular velocity and acceleration from very high-rate GNSS attitudes by applying regularization under the criterion of minimum mean squared errors. The major results from the experiments can be summarized in the following: (i) angular velocity and acceleration waveforms computed by applying the difference methods to high-rate GNSS attitudes are too noisy and can be physically not meaningful and numerically incorrect. The same can be said about inertial measurement unit (IMU) attitudes, if IMU gyros are not of very high accuracy; (ii) regularization is successfully applied to reconstruct the high-rate angular velocity and acceleration waveforms from 50 Hz GNSS attitudes and significantly outperforms the difference methods, validating the proposed concept of GNSS gyroscopes. By comparing the angular velocity and acceleration results by using the difference methods and regularization, we find that the peak values of angular velocity and acceleration by regularization are much smaller by a maximum factor of 1.57 in the angular velocity to a maximum factor of 8662.53 times in the angular acceleration in the case of high-rate GNSS, and by a maximum factor of 1.26 in the angular velocity to a maximum factor of 2819.85 times in the angular acceleration in the case of IMU, respectively; and (iii) the IMU attitudes apparently lead to better regularized angular velocity and acceleration waveforms than the high-rate GNSS attitudes, which can well be explained by the fact that the former is of better accuracy than the latter. As a result, to suppress the significant amplification of noise in GNSS attitudes, larger regularization parameters have to be chosen for the high-rate GNSS attitudes, resulting in smaller peak angular accelerations by a maximum factor of 37.55 percent in the angular velocity to a maximum factor of 6.20 times in the angular acceleration in comparison of the corresponding IMU results. Nevertheless, the regularized angular acceleration waveforms for both GNSS and IMU look more or less similar in pattern or waveform shape.

Vibration reliability of steel beams prestressed by drawing

Introduction. Vibrations of building structures and mechanism parts were analyzed. The need to investigate the oscillation processes and vibration reliability of steel beams prestressed by web drawing was formulated. The subject of study is structural steel. The object of study is bimetallic steel beam prestressed without rods.Materials and methods. The scientific inquiry is based on the basics of structural mechanics of buildings and structures: superposition principle, differential equation of deflection curve of a bar, energy method, and methods of determination of stress-strain state of prestressed steel bars.Results. A comparative analysis of vibration reliability of non-prestressed beams and prestressed structures of equal bearing capacity was performed. Rotations of the beam supporting nodes loaded by prestressing forces and external impacts were determined by integration of differential equation of deflection curve of a split bar. The support moments in rigid supporting nodes of structures were determined on the basis of superposition principle. The developed methods of stressed condition of prestressed bars are the basis for determination of normal stresses in the sections of beams under study. The resultant stresses were obtained by algebraic addition of prestresses and stresses from external loads. Dynamic parameters of bearing capacity of beams were determined on the basis of works by I.M. Rabinovich and V.A. Kiselev. The oscillation circular frequency of conventional and prestressed beams was established, analytical expressions for determination of angular velocity of prestressed bending elements were formulated, and the dynamic deflections and factors of structures were determined. It is found that the circular frequency of prestressed beams hinged in supporting nodes compared to the circular frequency of conventional beams decreases by a factor of 1.4 and by a factor of 5.6 in beams with rigid supports. Angular velocity decreases by a factor of 1.4 (hinge supports) and 6.8 (rigid supports), respectively. The deflections of prestressed beams are reduced by a factor of 1,87: 11,9. There is a significant reduction in the stressed condition of prestressed structures.Conclusions. A hinged traditional beam under external and vibration loads in limit state is in the material yield zone and does not meet the first and second limit state conditions. These structures have the lowest vibration reliability. Prestressed structures are more reliable. With rigid supporting nodes, the moments of prestressing forces coincide with the supporting moments and produce hogging with the vector opposite to the external load deflection vector. In the limit state, total deflections are less than the external load deflections. Stresses in the structure decrease. Since load moments and beam deflections are initial parameters for dealing with dynamic strength tasks, we may state that prestressed beams with rigid supporting nodes have an increased vibration reliability.

Optimal Rotational Angular Velocity Determination Method Based on Compound Rotary Semi-Strapdown Inertial Navigation System.

Single-axis rotation modulation (SRM) still accumulates errors in the roll axis direction, which leads to the navigation accuracy not meeting the requirements of guided missiles. Compound rotation modulation (CRM) superimposes one-dimensional rotation on the basis of SRM, so that the error of the projectile in the direction of the roll axis is also modulated. However, the error suppression effect of CRM is not only affected by the error of the IMU itself, but also related to the modulation angular velocity. In order to improve the accuracy of rotary semi-strapdown inertial navigation system (RSSINS), this paper proposes an optimal rotation angular velocity determination method. Firstly, the residual error in CRM scheme is analyzed; then, the relationship between the incomplete modulation error and the modulation angular velocity in CRM is discussed; finally, a method for determining the optimal modulation angular velocity is proposed (K-value method). The analysis of the results shows that the navigation accuracy of the guided projectile is effectively improved with the rotation scheme set at the modulation angular velocity determined by the K-value method.

Estimator-Based GPS Attitude and Angular Velocity Determination

In this paper, the estimator-based Global Positioning System (GPS) attitude and angular velocity determination is presented. Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities, depending on the design of estimator. Traditionally as a position, velocity and time sensor, the GPS also offers a free attitude-determination interferometer. GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted. The raw attitude solution using the interferometry technique based on the least-squares approach is inherently noisy. The estimator such as the Kalman filter (KF) or extended Kalman filter (EKF) can be incorporated into the GPS interferometer, potentially providing several advantages, such as accuracy improvement, reliability enhancement, and real-time characteristics. Three estimator-based approaches are investigated for performance comparison, including (1) KF with measurement involving attitude angles only; (2) EKF with measurements based on attitude angles only; (3) EKF with measurements involving both attitude angles and body angular rates. The assistance from body mounted gyroscopes, if available, can be utilized as the measurements for further performance improvement, especially useful for the case of signal-challenged environment, such as the GPS outages. Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented. Simulation results for various estimator-based approaches are conducted; performance comparison is presented for the case of GPS outages.

Method and implementation of micro Inertial Measurement Unit (IMU) in sensing basketball dynamics

In this paper, an Inertial Measurement Unit (IMU) is integrated with a basketball and used to measure basketball dynamics during various training and game exercises. We implemented an IMU composed of three-axis MEMS accelerometers and three-axis MEMS gyroscopes interfaced with a microcontroller on a basketball to measure basketball dynamics. Herein, methods are outlined for determining the rotational velocity of the basketball, namely backspin, and its axis of rotation during a shot which can be directly related to player shot form. Information about a player’s dribbling ability can also be discerned from the players dribbling frequency, captured through acceleration information. Our experimental validation shows that methods of angular velocity determination from both gyroscopes and accelerometers individually yield less than 2% error, making both methods viable in use. We also showed a method to detect the angle of the rotational axis relative to the ground. The methods outlined in this paper could be utilized to collect dynamic data that can be used to effectively train a basketball player and assist in skill improvements and benchmarking; all of which is valuable information for players and coaches alike.

Investigating the effects of quadrature error in parametrically and harmonically excited MEMS rate gyroscopes

Some factors like environmental conditions and manufacturing errors affect performance of a MEMS rate gyroscope. Because they may result to parameter mismatch between the designed gyroscope and the fabricated one. The Parametrically excited gyros are more robust to these changes than the harmonically excited gyros. However, these types of gyros also experience reduction in their accuracy in angular velocity determination due to these changes. One of parameters that affect the accuracy of the gyroscope is quadrature error that here, its effect in the accuracy of angular velocity determination is investigated in two typically designed harmonically and parametrically excited MEMS gyroscopes. The studies are done solving the gyroscopes’ equations analytically and numerically after addition of quadrature error. Finally, it’s found that the quadrature error reduces the accuracy of the gyroscope. Accuracy reduction (equivalent to output error increasing) decreases with increasing angular velocity or decreasing quadrature error almost the same for two types of gyroscope.

On the possibility of using the phase characteristic of a ring interferometer in microoptical gyroscopes

The prototype schemes of a microoptical gyroscope (MOG) developed to date on the basis of passive ring cavities imply the use of the amplitude characteristic only, since they operate using the dip in the transmission coefficient. We have analysed the possibility of creating a MOG, in which the phase characteristic is used as well. The phase characteristic of a ring interferometer has distinctive features in the vicinity of the cavity eigenfrequencies, which may be used to determine the angular velocity. A method for the angular velocity determination using both the phase and the amplitude characteristics of the interferometer is considered.

Confirmation of Arabia plate slow motion by new GPS data in Yemen

During the last 10 years, a network of about 30 GPS sites was measured in Djibouti, East Africa. Additional points were also measured in Yemen, Oman, Ethiopia, Iran, and on La Réunion island. Merged with data from the available International GPS Service permanent stations scattered on the different plates in the area (Eurasia, Anatolia, Africa, Arabia, Somalia), this unique data set provides new insight on the current deformation in the Africa‐Somalia‐Arabia triple junction area and on the Arabian plate motion. Here we show that coherent motions of points in Yemen, Bahrain, Oman, and Iran allow us to estimate a geodetically constrained angular velocity for the Arabian plate (52.59°N, 15.74°W, 0.461°/Myr in ITRF2000). This result differs significantly from earlier determinations and is based upon our vectors in Yemen. They provide new additional data and better geometry for angular velocity determination. Combined with the African and Somalian motions, this new angular velocity results in predicted spreading rates in the Red Sea and the Gulf of Aden which are 15–20% lower than those measured from oceanic magnetic anomalies and thus averaged over the last 3 Myr. With respect to Eurasia, the geodetic motion of Arabia is also about 30% slower than predicted by NUVEL‐1A. On the basis of the kinematic results presented here and on other evidence for a similar slower geodetic rate of the Indian plate, we suggest that the whole collision zone between Africa, Arabia, India on one hand and Eurasia on the other hand has slowed down in the last 3 Myr.

Determination of Angular Velocity and Accelerations of Human Elements Using Method of Spline Interpolation

Determination of Angular Velocity and Accelerations of Human Elements Using Method of Spline Interpolation

Synthesis of virtual measurements in nonlinear observation problem

AbstractThe method of the observation problems reducing to the algebraic ones is considered for the systems, which are linear with respect to unknown components of the phase vector. The approach proposed is based on the methods of the controlled stabilization of nonlinear system with respect to the part of variables. The equations of the initial observable system are supplemented by the equations of its controlled prototype. Then control law synthesied in such way that any given manifold becomes an invariant for extended system. For ensuring of this manifold attracting property the partial differential equations are obtained. Finally, the chosen in such way algebraic relations are considered as additional virtual measurements of unknown state. As example the problem of the angular velocity determination of a rigid body is considered. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of the cage induction motor for symmetrical and asymmetrical modes of operation

This paper presents a numerical model of the three-phase, cage induction motor. This model has been represented as a system of differential equations for flux linkages and angular velocity determination. The differential equations for the flux linkages of the stator windings have been expressed in phase coordinates, while the differential equations for the flux linkages of the rotor circuits have been expressed in orthogonal coordinates, which are fixed in respect with the stator of the motor. The skin effect in the rotor deep bars has been taken in account by representing the rotor as two parallel-connected resistive–inductive circuits. Using the developed model the starting, restarting, running-down modes and three-phase, line-to-line, line-to-ground short-circuits as well as the steady-state conditions can be analyzed. The modes of sudden three-phase short-circuit at the motor terminals, sudden single line-to-ground fault at the high-voltage side of the power supply system and the motor starting process followed by steady-state conditions have been computed.

A procedure for three-dimensional angular velocity determination using a star sensor in high-rate rotation modes

This paper presents an application for modern star trackers aimed at the estimation of the spacecraft angular velocity vector on the basis of the star field images acquired during fast rotations, when star identification and tracking are not possible. Angular rates in the range 2–8°/s are considered, which strongly affect the characteristics of the acquirable images, in particular for shape and brightness. The procedure consists in the exploitation of the rigid motion equations to identify the rotation that best fits the observed star trajectories in the sensor field of view. Its coverage capability is analysed with reference to the sensitivity of state-of-the-art photodetectors. The probability of an adequate acquisition is shown to be 0.80 with random pointing and rotation axis over the celestial sphere. Firstly, the accuracy of the procedure is discussed in numerical tests. Then, end-to-end tests are reported, which have been operated by implementing the procedure in a hardware sensor model that acquires simulated star field scenes in a laboratory facility. Both the validations point out that the accuracy of 1°/s, suggested by the European Space Agency for this kind of application, has been achieved. Moreover, the rate of rotation about axes perpendicular to the boresight can be computed with accuracy one order of magnitude better.

Direct Determination of Angular Velocity Using GPS

Controlling a ship in a berthing operation is carried out mainly by the change of state, such as velocity and yaw rate (turn rate), although the value of the change of state is very small at berthing. Very high precision is, therefore, required to determine the velocity and angular velocity. A sensor that has an accuracy of ±0.02°/s (1 σ) is sought for determination of turn rate in a berthing system. Three-dimensional angular velocity can directly be determined, with 2 independent baselines of 3 GPS antennas, using instantaneous Doppler measurements or phase rate (temporal difference of phase) observations. This paper discusses the mathematical model for direct determination of angular velocity using GPS, and the comparison of the results of the angular velocity determination using the Doppler and phase rate. The precision of angular velocity determination is estimated using temporal difference of the attitude sensors (TSS and gyrocompass) on board a hydrographic sounding ship. The RMS values of the difference of yaw rate determination between the two systems were: ±0.16°/s using phase rate and ±0.31°/s using Doppler measurements with the separation of onboard antennas of ca. 1·34 m. 10 m baselines could satisfy the sensor requirements for angular velocity determination during berthing maneuvers.

A Simple Method for the Determination of Angular Velocity and Acceleration of a Spherical Motion Through Quaternions

Given a quaternion representation of a spherical motion of a rigid body with respect to another body, acting as a reference frame, this contribution presents a simple and straightforward method for determining both the angular velocity and angular acceleration of the moving body with respect to the reference frame. Instead of employing orthogonal matrices or their linear invariants, this contribution makes use of quaternions avoiding, in this way, the series of matrix identities or theorems that are required in a pair of previous approaches.

Exploiting sound absorption for target motion analysis

Normally, sound level as a function of time originating from a target moving with constant (and, compared to the speed of sound, small) velocity, only permits the determination of angular velocity. However, sound absorption becoming important in the ultrasonic region can be exploited to estimate both target velocity and range. The theoretical estimation accuracy is investigated employing model assumptions of increasing complexity, including the exploitation of possibly available measurements of target bearing angle. The proposed procedures are applied to both simulated and real data.

Rigid-Body Rotor Dynamics: Dynamic Unbalance and Lubricant Temperature Changes

The case of a symmetric rotor supported on two identical, rigidly mounted, self-aligning, finite-length (L/D = 1) fluid-film journal bearings is considered. Rotor position is described by two translation coordinates in a plane perpendicular to the bearing line of centers, and by three Euler angles. Introduction of various amounts of dynamic unbalance via the inertia tensor off-diagonal terms (products of inertia) allows determination of angular velocity and static eccentricity ratio combinations leading to bearing “failure” defined for arbitrary maximum allowable eccentricity ratios. Instability hysteresis, defined here as the persistence, during rotor deceleration, of instability to speeds below which it first appeared, is considered by means of the above model. Equations and methods developed for the unbalance investigation are adapted to a variable-speed analysis. With both constant and variable mean bearing temperatures, variable-speed simulations terminating at constant speed are observed to be stable when the terminating point is below the instability threshold curve on the angular velocity-static eccentricity ratio parameter plane and unstable when above. The slope of the threshold curve and the shape of the equilibrium-condition path on the parameter plane (single-line path for constant temperature, closed curve for variable temperature) apparently combine to produce hysteresis in the variable temperature case and none at constant temperature.