A Unified Coordinate System for Solving the Three-Dimensional Euler Equations

2001 ◽  
Vol 172 (1) ◽  
pp. 235-260 ◽  
Author(s):  
W.H. Hui ◽  
S. Kudriakov
Keyword(s):  
Coordinate System ◽  
Euler Equations ◽  
Three Dimensional ◽  
Unified Coordinate System

The Establishment of Unified Coordinate System in Microtarget-Automatic-Assembly System

2011 ◽  
Vol 347-353 ◽  
pp. 1454-1457
Author(s):  
Xing Hua Li ◽  
Hai Qiang Wang
Keyword(s):  
Coordinate System ◽  
Inertial Confinement Fusion ◽  
Three Dimensional ◽  
Assembly System ◽  
Inertial Confinement ◽  
Microscopic Image ◽  
Automatic Assembly ◽  
Image Measurement ◽  
Confinement Fusion ◽  
Unified Coordinate System

There are three subsystems in Microtarget-Automatic-Assembly System which is used in Inertial Confinement Fusion(ICF). It is microscopic image measurement subsystem,confocal probe measurement subsystem and three-dimensional motion subsystem. It is necessary to establish a unified coordinate system in order to interact information in three subsystems and provide accurate and reliable position and attitude information for micro-operating system.Each coordinate system and its errors are analyzed in this paper.In the end,the way to establish the unified coordinate system is given. It is proved that this subsystem meets the requirements for precision.

Analysis of three-dimensional aerospace configurations using the Euler equations

1989 ◽  
Author(s):  
N. KROLL ◽  
C. ROSSOW ◽  
S. SCHERR ◽  
J. SCHOENE ◽  
G. WICHMANN
Keyword(s):  
Euler Equations ◽  
Three Dimensional

Comparison Considerations Toward Investigating the Factors of Load and Age Group on the Maximum Reach Envelope

2020 ◽  
pp. 001872082096501
Author(s):  
Heather Johnston ◽  
Colleen Dewis ◽  
John Kozey
Keyword(s):  
Coordinate System ◽  
Three Dimensional ◽  
Spherical Coordinate System ◽  
Upper Body ◽  
Group Differences ◽  
Anthropometric Measures ◽  
Younger Adults ◽  
Present Measurement ◽  
Spherical Coordinate ◽  
Cylindrical Coordinate

Objective The objectives were to compare cylindrical and spherical coordinate representations of the maximum reach envelope (MRE) and apply these to a comparison of age and load on the MRE. Background The MRE is a useful measurement in the design of workstations and quantifying functional capability of the upper body. As a dynamic measure, there are human factors that impact the size, shape, and boundaries of the MRE. Method Three-dimensional reach measures were recorded using a computerized potentiometric system for anthropometric measures (CPSAM) on two adult groups (aged 18–25 years and 35–70 years). Reach trials were performed holding .0, .5, and 1 kg. Results Three-dimensional Cartesian coordinates were transformed into cylindrical ( r, θ , Z) and spherical ( r, θ, ϕ) coordinates. Median reach distance vectors were calculated for 54 panels within the MRE as created by incremented banding of the respective coordinate systems. Reach distance and reach area were compared between the two groups and the loaded conditions using a spherical coordinate system. Both younger adults and unloaded condition produced greater reach distances and reach areas. Conclusions Where a cylindrical coordinate system may reflect absolute reference for design, a normalized spherical coordinate system may better reflect functional range of motion and better compare individual and group differences. Age and load are both factors that impact the MRE. Application These findings present measurement considerations for use in human reach investigation and design.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Nonlinear Axisymmetric Deformation Model for Structures of Revolution

2011 ◽  
Vol 3 (4) ◽  
pp. 420-447
Author(s):  
Ayman Mourad ◽  
Jawad Zaarour
Keyword(s):  
Coordinate System ◽  
Three Dimensional ◽  
Axisymmetric Deformation ◽  
Large Displacement ◽  
Deformation Model ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Cylindrical Coordinate ◽  
Mathematical Derivation ◽  
Displacement Effects

AbstractAn axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented. The axisymmetric deformation model is described using the cylindrical coordinate system. Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation. Mathematical derivation of the formulation is given, and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.

Interstitial Nucleus of Cajal Encodes Three-Dimensional Head Orientations in Fick-Like Coordinates

2007 ◽  
Vol 97 (1) ◽  
pp. 604-617 ◽  
Author(s):  
Eliana M. Klier ◽  
Hongying Wang ◽  
J. Douglas Crawford
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Semicircular Canals ◽  
Head Rotation ◽  
Head Orientation ◽  
Interstitial Nucleus Of Cajal ◽  
The Gaze ◽  
Behavioral Constraints ◽  
The Right

Two central, related questions in motor control are 1) how the brain represents movement directions of various effectors like the eyes and head and 2) how it constrains their redundant degrees of freedom. The interstitial nucleus of Cajal (INC) integrates velocity commands from the gaze control system into position signals for three-dimensional eye and head posture. It has been shown that the right INC encodes clockwise (CW)-up and CW-down eye and head components, whereas the left INC encodes counterclockwise (CCW)-up and CCW-down components, similar to the sensitivity directions of the vertical semicircular canals. For the eyes, these canal-like coordinates align with Listing’s plane (a behavioral strategy limiting torsion about the gaze axis). By analogy, we predicted that the INC also encodes head orientation in canal-like coordinates, but instead, aligned with the coordinate axes for the Fick strategy (which constrains head torsion). Unilateral stimulation (50 μA, 300 Hz, 200 ms) evoked CW head rotations from the right INC and CCW rotations from the left INC, with variable vertical components. The observed axes of head rotation were consistent with a canal-like coordinate system. Moreover, as predicted, these axes remained fixed in the head, rotating with initial head orientation like the horizontal and torsional axes of a Fick coordinate system. This suggests that the head is ordinarily constrained to zero torsion in Fick coordinates by equally activating CW/CCW populations of neurons in the right/left INC. These data support a simple mechanism for controlling head orientation through the alignment of brain stem neural coordinates with natural behavioral constraints.

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