On the angular velocity of a rigid body: Matrix and vector representations

2014 ◽  
Vol 45 ◽  
pp. 123-132
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
José M. Rico-Martínez ◽  
Victor Hugo Pérez-Muñoz
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Vector Representations

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

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.

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