Sensor Placement for Angular Velocity Determination

2005 ◽  
Vol 128 (3) ◽  
pp. 543-547 ◽  
Author(s):  
Guy M. Genin ◽  
Joseph Genin
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
Constraint Equation ◽  
Complete Characterization ◽  
Angular Velocity Vector ◽  
Algebraic Constraint ◽  
Transducer Placement

Velocity transducer placement to uniquely determine the angular velocity of a rigid body is investigated. The angular velocity of a rigid body can be determined with no fewer than five properly placed velocity transducers, if no other types of sensors are present and no algebraic constraint equation involving the angular velocity vector can be written. Complete characterization of the velocity of a rigid body requires six transducers. Choice of transducer placement and orientation requires care, as suboptimal transducer placement can result in data from which the determination of a unique angular velocity vector is impossible. Conditions for successful transducer placement are established, and two examples of adequate transducer placement are presented: an Earth-penetrating projectile, and a bioengineering device for the measurement of head motion.

Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions

2018 ◽  
Vol 19 (12) ◽  
pp. 10-17587/mau.19.797-805
Author(s):  
Ya. G. Sapunkov ◽  
A. V. Molodenkov ◽  
T. V. Molodenkova
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
Space Shuttle ◽  
Control Function ◽  
Axially Symmetric ◽  
Bounded Control ◽  
Angular Velocity Vector ◽  
Time Optimal ◽  
Optimal Turn

The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

scholarly journals On New Modifications of Some Perturbation Procedures

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
The Body ◽  
Large Parameter ◽  
Angular Velocity Vector ◽  
Rigid Body Dynamic ◽  
Motion Problem ◽  
Slow Motions ◽  
Body Dynamic

In this paper, we present new modifications for some perturbation procedures used in mathematics, physics, astronomy, and engineering. These modifications will help us to solve the previous problems in different sciences under new conditions. As problems, we have, for example, the rotary rigid body problem, the gyroscopic problem, the pendulum motion problem, and other ones. These problems will be solved in a new manner different from the previous treatments. We solve some of the previous problems in the presence of new conditions, new analysis, and new domains. We let complementary conditions of such studied previously. We solve these problems by applying the large parameter technique used by assuming a large parameter which inversely proportional to a small quantity. For example, in rigid body dynamic problems, we take such quantity to be one of the components of the angular velocity vector in the initial instant of the rotary body about a fixed point. The domain of our solutions will be depending on the choice of a large parameter. The problem of slow (weak) oscillations is considered. So, we obtain slow motions of the bodies instead of fast motions and find the solutions of the problem in present new conditions on both of center of gravity, moments of inertia, and the angular velocity vector or one of these parameters of the body. This study is important for aerospace engineering, gyroscopic motions, satellite motion which has the correspondence of inertia moments, antennas, and navigations.

Determination of the Angular Velocity Vector in Orthogonal Curvilinear Coordinate Systems

1992 ◽  
Vol 59 (2) ◽  
pp. 456-457 ◽  
Author(s):  
D. L. Richardson
Keyword(s):  
Angular Velocity ◽  
Velocity Vector ◽  
General Procedure ◽  
Coordinate Systems ◽  
Angular Velocity Vector ◽  
Coordinate Frames ◽  
Curvilinear Coordinate

An efficient, general procedure is developed for assembling the components of the angular velocity vector of orthogonal curvilinear coordinate frames

Photoluminescence Excitation Spectroscopy of Carbon-Doped Gallium Nitride

1998 ◽  
Vol 537 ◽  
Author(s):  
E. E. Reuter ◽  
R. Zhang ◽  
T. F. Kuech ◽  
S. G. Bishop
Keyword(s):  
Complete Characterization ◽  
Photoluminescence Excitation ◽  
Yellow Luminescence ◽  
Broad Excitation Band ◽  
Carbon Doped ◽  
Sapphire Substrates ◽  
Red Luminescence ◽  
Unusual Shape

AbstractWe have done a comparative study of carbon-doped GaN and undoped GaN utilizing photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopies in order to investigate deep levels involved in yellow luminescence (YL) and red luminescence (RL). When the GaN was excited by above-bandgap light, red luminescence (RL) centered at 1.82 eV was the dominant below-gap PL from undoped GaN, but carbon-doped GaN below-gap PL was dominated by yellow luminescence (YL) centered at 2.2 eV. When exciting PL below the band-gap with 2.4 eV light, undoped GaN had a RL peak centered at 1.5 eV and carbon-doped GaN had a RL peak centered at 1.65 eV. PLE spectra of carbon-doped GaN, detecting at 1.56 eV, exhibited a strong, broad excitation band extending from about 2.1 to 2.8 eV with an unusual shape that may be due to two or more overlapping excitation bands. This RL PLE band was not observed in undoped GaN. We also demonstrate that PL spectra excited by below gap light in GaN films on sapphire substrates are readily contaminated by 1.6-1.8 eV and 2.1-2.5 eV chromium-related emission from the substrate. A complete characterization of the Cr emission and excitation bands for sapphire substrates enables the determination of the excitation and detection wavelengths required to obtain GaN PL and PLE spectra that are free of contributions from substrate emission.

scholarly journals Isometric and Closed-Range Composition Operators between Bloch-Type Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Nina Zorboska
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Function Spaces ◽  
Complete Characterization ◽  
Closed Range ◽  
Different Types ◽  
Type Spaces ◽  
Range Determination

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

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