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Vectors and Relative Velocity

The Mathematical Gazette, 1969
In many books on elementary mechanics, it is assumed that velocity is a vector quantity on the grounds that it has magnitude and direction. It is, however, very far from obvious that these are sufficient reasons and a rather more thorough investigation of the nature of velocity may provide not only a clearer idea of what velocity is but may also clear ...
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Rigid velocities compatible with five image velocity vectors

Image and Vision Computing, 1989
Abstract The problem of obtaining rigid velocities compatible with a given set of image velocity vectors is algebraic in that it depends on the solution of simultaneous polynomial equations. We show that five image velocity vectors yield two quartic polynomial constraints on the translational part of the rigid velocity, and that of the 16 common ...
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Velocity vector roll control

Guidance, Navigation, and Control Conference, 1996
This paper is devoted to the challenging problem of high angle of attack and maneuvering flight control, with special emphasis on the critical velocity vector roll maneuver. The development of a flight control system for maneuvering flight, i.e., high amplitude maneuvers, requires careful modeling.
M. Pachter, P. Chandler
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Anticipating adolescent growth vectors and velocities

American Journal of Orthodontics, 1972
Abstract Growth potency can be evaluated by the hand-wrist radiograph, standards of height-weight values, and serial cephalometric observation radiographs. Experience adapts accepted predictive charts, such as those of Bayer and Bayley, to the norms of any ethnic population for the individual patients under treatment.
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Vector of Coordinates, Velocities and Accelerations

2015
This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with
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Velocity Gradient Method of Lyapunov Vector Functions

Proceedings of the 2019 the 5th International Conference on e-Society, e-Learning and e-Technologies - ICSLT 2019, 2019
In this paper, a new approach for constructing the Lyapunov function is considered. Lyapunov function is obtained as a vector function on the basis of the geometric interpretation of the Lyapunov's second method and, its antigradient is given by the velocity vector components (the right-hand side of the state equation) of the system. The stability area
Mamyrbek Beisenbi   +3 more
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Multizone reproduction by matching the velocity vectors

The Journal of the Acoustical Society of America, 2023
This paper proposes a velocity-based multizone reproduction method, which reproduces the velocity vectors throughout each listening zone. Velocity vectors are related to the localization of sound below 700 Hz. Previous work considered reproducing the velocity vectors at sweet spots or on the listening zone’s boundary, and usually involved measurements ...
Jiarui Wang   +3 more
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Examples of Vector Velocity Imaging

2011
To measure blood flow velocity in vessels with conventional ultrasound, the velocity is estimated along the direction of the emitted ultrasound wave. It is therefore impossible to obtain accurate information on blood flow velocity and direction, when the angle between blood flow and ultrasound wave approaches 90°.
Peter M. Hansen   +4 more
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Examples of In Vivo Blood Vector Velocity Estimation

Ultrasound in Medicine & Biology, 2007
In this paper, a case study of in-vivo blood vector velocity images of the carotid artery are presented. The transverse oscillation (TO) method for blood vector velocity estimation has been used to estimate the vector velocities. The carotid arteries of three healthy volunteers are scanned in-vivo at three different positions by experienced ...
Udesen, Jesper   +3 more
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A new digital algorithm for the velocity translation vector

Science China Information Sciences, 2013
The error of the conventional sculling correction algorithm under maneuvers is analyzed through Taylor series expansion; a generalized error equation is presented. Using frequency-series sculling algorithms in the digital algorithm for the velocity translation vector will cause the accuracy of the digital algorithm under maneuvers to decrease by one ...
Min Song, Wenqi Wu
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