scholarly journals Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

2013 ◽  
Vol 139 (17) ◽  
pp. 174108 ◽  
Author(s):  
Alexander Semenov ◽  
Dmitri Babikov
Keyword(s):  
Inelastic Scattering ◽  
Classical Theory ◽  
Reference Frames ◽  
Fixed Reference

Using K’NEX to Understand and Teach Concepts in Movement Biomechanics

2010 ◽  
Author(s):  
Steven Charles
Keyword(s):  
Lower Limb ◽  
Reference Frames ◽  
Human Motion ◽  
The Body ◽  
Single Degree Of Freedom ◽  
Generalized Coordinates ◽  
Single Degree ◽  
Fixed Reference ◽  
Time To Learn ◽  
And Robotics

In order to analyze the kinematics or model the dynamics of human motion, one must be able to abstract from the intricate anatomy of the body the mechanical linkages and kinematic constraints which best approximate the joints of the body. Given the number and complexity of joints in the human body, this abstraction can be a challenging task, especially for students. While rotations about a single degree of freedom are easy to grasp, rotations about multiple DOF, which occur commonly throughout the body (e.g. shoulder, wrist, ankle, etc.) are anything but trivial. Likewise, the kinematics or dynamics of mechanical linkages such as the upper or lower limb quickly become unwieldy. To deal with these challenges, students learn to use tools from mechanics and robotics (body- and space-fixed reference frames, transformations, generalized coordinates, etc.), but these concepts can themselves be challenging and certainly take time to learn.

Be´zier Curves on Riemannian Manifolds and Lie Groups with Kinematics Applications

1995 ◽  
Vol 117 (1) ◽  
pp. 36-40 ◽  
Author(s):  
F. C. Park ◽  
B. Ravani
Keyword(s):  
Riemannian Manifold ◽  
Rigid Body ◽  
Lie Groups ◽  
Riemannian Manifolds ◽  
Reference Frames ◽  
Group Structure ◽  
Recursive Algorithm ◽  
Fixed Reference ◽  
Spatial Displacements ◽  
Natural Way

In this article we generalize the concept of Be´zier curves to curved spaces, and illustrate this generalization with an application in kinematics. We show how De Casteljau’s algorithm for constructing Be´zier curves can be extended in a natural way to Riemannian manifolds. We then consider a special class of Riemannian manifold, the Lie groups. Because of their group structure Lie groups admit an elegant, efficient recursive algorithm for constructing Be´zier curves. Spatial displacements of a rigid body also form a Lie group, and can therefore be interpolated (in the Be´zier sense) using this recursive algorithm. We apply this alogorithm to the kinematic problem of trajectory generation or motion interpolation for a moving rigid body. The orientation trajectory of motions generated in this way have the important property of being invariant with respect to choices of inertial and body-fixed reference frames.

Roles of Gravitational Cues and Efference Copy Signals in the Rotational Updating of Memory Saccades

2005 ◽  
Vol 94 (1) ◽  
pp. 468-478 ◽  
Author(s):  
Eliana M. Klier ◽  
Dora E. Angelaki ◽  
Bernhard J. M. Hess
Keyword(s):  
Reference Frames ◽  
Target Location ◽  
Body Position ◽  
Upright Position ◽  
Original Position ◽  
Fixed Target ◽  
3 Dimensional ◽  
Fixed Reference ◽  
Inertial Cues ◽  
Passive Movements

Primates are able to localize a briefly flashed target despite intervening movements of the eyes, head, or body. This ability, often referred to as updating, requires extraretinal signals related to the intervening movement. With active roll rotations of the head from an upright position it has been shown that the updating mechanism is 3-dimensional, robust, and geometrically sophisticated. Here we examine whether such a rotational updating mechanism operates during passive motion both with and without inertial cues about head/body position in space. Subjects were rotated from either an upright or supine position, about a nasal–occipital axis, briefly shown a world-fixed target, rotated back to their original position, and then asked to saccade to the remembered target location. Using this paradigm, we tested subjects' abilities to update from various tilt angles (0, ±30, ±45, ±90°), to 8 target directions and 2 target eccentricities. In the upright condition, subjects accurately updated the remembered locations from all tilt angles independent of target direction or eccentricity. Slopes of directional errors versus tilt angle ranged from −0.011 to 0.15, and were significantly different from a slope of 1 (no compensation for head-in-space roll) and a slope of 0.9 (no compensation for eye-in-space roll). Because the eyes, head, and body were fixed throughout these passive movements, subjects could not use efference copies or neck proprioceptive cues to assess the amount of tilt, suggesting that vestibular signals and/or body proprioceptive cues suffice for updating. In the supine condition, where gravitational signals could not contribute, slopes ranged from 0.60 to 0.82, indicating poor updating performance. Thus information specifying the body's orientation relative to gravity is critical for maintaining spatial constancy and for distinguishing body-fixed versus world-fixed reference frames.

Roll-Dependent Modulation of the Subjective Visual Vertical: Contributions of Head- and Trunk-Based Signals

2010 ◽  
Vol 103 (2) ◽  
pp. 934-941 ◽  
Author(s):  
A. A. Tarnutzer ◽  
C. J. Bockisch ◽  
D. Straumann
Keyword(s):  
Reference Frame ◽  
Sensory Input ◽  
Reference Frames ◽  
Longitudinal Axis ◽  
Subjective Visual Vertical ◽  
Lateral Tilt ◽  
Accuracy And Precision ◽  
Visual Vertical ◽  
Fixed Reference ◽  
Precision And Accuracy

Precision and accuracy of the subjective visual vertical (SVV) modulate in the roll plane. At large roll angles, systematic SVV errors are biased toward the subject's body-longitudinal axis and SVV precision is decreased. To explain this, SVV models typically implement a bias signal, or a prior, in a head-fixed reference frame and assume the sensory input to be optimally tuned along the head-longitudinal axis. We tested the pattern of SVV adjustments both in terms of accuracy and precision in experiments in which the head and the trunk reference frames were not aligned. Twelve subjects were placed on a turntable with the head rolled about 28° counterclockwise relative to the trunk by lateral tilt of the neck to dissociate the orientation of head- and trunk-fixed sensors relative to gravity. Subjects were brought to various positions (roll of head- or trunk-longitudinal axis relative to gravity: 0°, ±75°) and aligned an arrow with perceived vertical. Both accuracy and precision of the SVV were significantly ( P < 0.05) better when the head-longitudinal axis was aligned with gravity. Comparing absolute SVV errors for clockwise and counterclockwise roll tilts, statistical analysis yielded no significant differences ( P > 0.05) when referenced relative to head upright, but differed significantly ( P < 0.001) when referenced relative to trunk upright. These findings indicate that the bias signal, which drives the SVV toward the subject's body-longitudinal axis, operates in a head-fixed reference frame. Further analysis of SVV precision supports the hypothesis that head-based graviceptive signals provide the predominant input for internal estimates of visual vertical.

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