Closure to “Discussion of ‘A Linear Algebra Approach to the Analysis of Rigid Body Velocity from Position and Velocity Data’” (1984, ASME J. Dyn. Syst., Meas., Control, 106, p. 240)

1984 ◽  
Vol 106 (3) ◽  
pp. 240-241
Author(s):  
A. J. Laub ◽  
G. R. Shiflett
Keyword(s):  
Rigid Body ◽  
Linear Algebra ◽  
Velocity Data ◽  
Algebra Approach ◽  
Body Velocity

A Linear Algebra Approach to the Analysis of Rigid Body Velocity From Position and Velocity Data

1983 ◽  
Vol 105 (2) ◽  
pp. 92-95 ◽  
Author(s):  
A. J. Laub ◽  
G. R. Shiflett
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Matrix Theory ◽  
The Body ◽  
Instantaneous Velocity ◽  
Body Motion ◽  
Translational Velocity ◽  
Velocity Data ◽  
Algebra Approach ◽  
Body Velocity

The instantaneous velocity of a rigid body in space is characterized by an angular and translational velocity. By representing the angular velocity as a matrix and the translational component as a vector the velocity of any point in the rigid body may be found if the position of the point and the parameters of the angular and translational velocities are known. Alternatively, the parameters of the rigid body velocity may be determined if the velocity and position of three points fixed in the body are known. In this paper, a new matrix-theory-based method is derived for determining the instantaneous velocity parameters of rigid body motion in terms of the velocity and position of three noncollinear points fixed in the body. The method is shown to possess certain advantages over traditional vectoral solutions to the same problem.

A Linear Algebra Approach to the Analysis of Rigid Body Displacement From Initial and Final Position Data

1982 ◽  
Vol 49 (1) ◽  
pp. 213-216 ◽  
Author(s):  
A. J. Laub ◽  
G. R. Shiflett
Keyword(s):  
Rigid Body ◽  
Linear Algebra ◽  
Initial Position ◽  
The Body ◽  
Final Position ◽  
Explicit Formulas ◽  
Algebra Approach ◽  
Other Information ◽  
Position Data ◽  
Rigid Body Displacement

The location and orientation of a rigid body in space can be defined in terms of three noncollinear points in the body. As the rigid body is moved through space, the motion may be described by a series of rotations and translations. The sequence of displacements may be conveniently represented in matrix form by a series of displacement matrices that describe the motion of the body between successive positions. If the rotations and translations (and hence the displacement matrix) are known then succeeding positions of a rigid body may be easily calculated in terms of the initial position. Conversely, if successive positions of three points in the rigid body are known, it is possible to calculate the parameters of the corresponding rotation and translation. In this paper, a new solution is presented which provides explicit formulas for the rotation and translation of a rigid body in terms of the initial and final positions of three points fixed in the rigid body. The rotation matrix is determined directly whereupon appropriate rotation angles and other information can subsequently be calculated if desired.

scholarly journals A linear algebra approach to minimal convolutional encoders

1993 ◽  
Vol 39 (4) ◽  
pp. 1219-1233 ◽  
Author(s):  
R. Johannesson ◽  
Z.-x. Wan
Keyword(s):  
Linear Algebra ◽  
Algebra Approach ◽  
Convolutional Encoders
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