scholarly journals Comment on ’’Theory of collisions between an atom and a diatomic molecule in the body‐fixed coordinate system

1979 ◽  
Vol 70 (6) ◽  
pp. 3151-3153 ◽  
Author(s):  
George C. Schatz ◽  
Aron Kuppermann
Keyword(s):  
Coordinate System ◽  
Diatomic Molecule ◽  
The Body ◽  
Body Fixed Coordinate System

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

2-D Inverse Dynamics Knee Model: Aligning Anatomical Knee Model With Knee Extension Kinematic Data Using Ligament Forces

2018 ◽  
Author(s):  
Jose Mario Salinas ◽  
Dumitru I. Caruntu
Keyword(s):  
Experimental Data ◽  
Coordinate System ◽  
Inverse Dynamics ◽  
Knee Extension ◽  
The Body ◽  
Body Segment ◽  
Center Of Rotation ◽  
Axis Of Rotation ◽  
Instantaneous Center ◽  
Body Fixed Coordinate System

This paper deals with aligning knee geometrical anatomical data with kinematic data from experimental work in order to develop a two-dimensional inverse dynamics anatomical model of human knee. Motion capture cameras were used to collect the experimental data for a knee extension exercise. Reflective markers were placed on the subjects’ skin during the experiment. In this model, joints such as hip, knee, and ankle are represented by axes of rotation. These axes are determined by calculating the relative instantaneous center of rotation of one body segment with respect to an adjacent body segment. Body-fixed coordinate systems were defined using three reflective markers attached to the subject. The origin of each body fixed-coordinate system was located between the three markers on that body segment, the body-fixed x-axis was pointing towards the marker on the lateral side of the body segment, and the body-fixed y-axis fell on the same plane as the three reflective markers on the body segment. Moreover, the axis of rotation that represents the hip was determined by calculating the instantaneous center of rotation of reflective markers located on the pelvis with respect to a body fixed coordinate system on the thigh. The axis of rotation on the knee was determined by calculating the instantaneous center of rotation of reflective markers on the shin (tibia) with respect to the body-fixed coordinate system on the thigh (femur). The axis of rotation on the ankle was determined by calculating the instantaneous center of rotation of reflective markers on the shin with respect to a body-fixed coordinate system on the foot. Bone anatomical geometries of femur and tibia were represented mathematically as polynomials and superimposed over the experimental data. This was done by matching the center of rotation from experimental data with the geometric center of the femoral condyle. This is necessary for estimating the insertions/origins of knee ligaments. These ligaments are modeled as nonlinear elastic springs. Furthermore, ligaments were divided into separate fiber bundles. Both the posterior and anterior cruciate ligaments were divided into an anterior and posterior fiber bundle. The cruciate ligament forces for both exercises are discussed in this paper.

Pose estimation of a fast tumbling space noncooperative target using the time-of-flight camera

2021 ◽  
pp. 095441002110002
Author(s):  
Qi-shuai Wang ◽  
Guo-ping Cai
Keyword(s):  
Coordinate System ◽  
Pose Estimation ◽  
Point Cloud ◽  
Time Of Flight ◽  
Point Clouds ◽  
The Body ◽  
Geometric Characteristics ◽  
Pose Tracking ◽  
Plane Point ◽  
Body Fixed Coordinate System

This article proposes a pose estimation method for a fast tumbling space noncooperative target. The core idea of this method is to extract the target’s body-fixed coordinate system by using the geometric characteristics of the target’s point cloud and then by the body-fixed coordinate system to realize pose initialization and pose tracking of the target. In the extraction of the body-fixed coordinate system, a point cloud of the target, which can be obtained by a time-of-flight camera, can be divided into small plane point clouds firstly; then the geometric information of these plane point clouds can be utilized to extract the target’s descriptive structures, such as the target surfaces and the solar panel supports; and finally the body-fixed coordinate system can be determined by the geometric characteristics of these structures. The body-fixed coordinate system obtained above can be used to determine the pose of consecutive point clouds of the target, that is, to realize the pose initialization and the pose tracking, and accumulated bias often emerges in the pose tracking. To mitigate the accumulated bias, a pose graph optimization method is adopted. In the end of this article, the performance of the proposed method is evaluated by numerical simulations. Simulation results show that when the distance between the target and the chaser is 10 m, the errors of the estimation results of the target’s attitude and position are 0.025° and 0.026 m, respectively. This means that the proposed method can achieve high-precision pose estimation of the noncooperative target.

scholarly journals Computation of electrostatic fields in anisotropic human tissues using the Finite Integration Technique (FIT)

2005 ◽  
Vol 2 ◽  
pp. 309-313 ◽  
Author(s):  
V. C. Motresc ◽  
U. van Rienen
Keyword(s):  
Coordinate System ◽  
Electromagnetic Fields ◽  
Human Body ◽  
Local Coordinate System ◽  
Anisotropic Materials ◽  
The Body ◽  
Integration Technique ◽  
Data Set ◽  
Computer Data ◽  
Finite Integration Technique

Abstract. The exposure of human body to electromagnetic fields has in the recent years become a matter of great interest for scientists working in the area of biology and biomedicine. Due to the difficulty of performing measurements, accurate models of the human body, in the form of a computer data set, are used for computations of the fields inside the body by employing numerical methods such as the method used for our calculations, namely the Finite Integration Technique (FIT). A fact that has to be taken into account when computing electromagnetic fields in the human body is that some tissue classes, i.e. cardiac and skeletal muscles, have higher electrical conductivity and permittivity along fibers rather than across them. This property leads to diagonal conductivity and permittivity tensors only when expressing them in a local coordinate system while in a global coordinate system they become full tensors. The Finite Integration Technique (FIT) in its classical form can handle diagonally anisotropic materials quite effectively but it needed an extension for handling fully anisotropic materials. New electric voltages were placed on the grid and a new averaging method of conductivity and permittivity on the grid was found. In this paper, we present results from electrostatic computations performed with the extended version of FIT for fully anisotropic materials.

scholarly journals How visual experience and task context modulate the use of internal and external spatial coordinate for perception and action

2018 ◽  
Author(s):  
Virginie Crollen ◽  
Tiffany Spruyt ◽  
Pierre Mahau ◽  
Roberto Bottini ◽  
Olivier Collignon
Keyword(s):  
Coordinate System ◽  
Visual Experience ◽  
Simon Task ◽  
Frame Of Reference ◽  
The Body ◽  
Blind People ◽  
Coordinate Systems ◽  
Task Instructions ◽  
Congenitally Blind ◽  
External Frame

Recent studies proposed that the use of internal and external coordinate systems may be more flexible in congenitally blind when compared to sighted individuals. To investigate this hypothesis further, we asked congenitally blind and sighted people to perform, with the hands uncrossed and crossed over the body midline, a tactile TOJ and an auditory Simon task. Crucially, both tasks were carried out under task instructions either favoring the use of an internal (left vs. right hand) or an external (left vs. right hemispace) frame of reference. In the internal condition of the TOJ task, our results replicated previous findings (Röder et al., 2004) showing that hand crossing only impaired sighted participants’ performance, suggesting that blind people did not activate by default a (conflicting) external frame of reference. However, under external instructions, a decrease of performance was observed in both groups, suggesting that even blind people activated an external coordinate system in this condition. In the Simon task, and in contrast with a previous study (Roder et al., 2007), both groups responded more efficiently when the sound was presented from the same side of the response (‘‘Simon effect’’) independently of the hands position. This was true under the internal and external conditions, therefore suggesting that blind and sighted by default activated an external coordinate system in this task. All together, these data comprehensively demonstrate how visual experience shapes the default weight attributed to internal and external coordinate systems for action and perception depending on task demand.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

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