Orbital Angular Momentum Operator in Spherical Coordinate System

1966 ◽  
Vol 34 (6) ◽  
pp. 537-537
Author(s):  
Y. F. Bow
Keyword(s):  
Angular Momentum ◽  
Coordinate System ◽  
Orbital Angular Momentum ◽  
Spherical Coordinate System ◽  
Momentum Operator ◽  
Angular Momentum Operator ◽  
Spherical Coordinate ◽  
Orbital Angular Momentum Operator

scholarly journals GLUEBALL SPIN

2001 ◽  
Vol 16 (01) ◽  
pp. 41-51
Author(s):  
D. SINGLETON
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Momentum Operator ◽  
Angular Momentum Operator ◽  
Total Field ◽  
Expectation Value ◽  
Starting Point ◽  
Simplifying Assumptions

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is re-examined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the possible restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This analysis can be compared to the electromagnetic charge/monopole system, where the requirement that the total field angular momentum obey the angular momentum commutation relationships places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of the field angular momentum operator under some simplifying assumptions.

Orbital angular momentum eigenfunctions for many-particle systems

1985 ◽  
Vol 63 (7) ◽  
pp. 1719-1722 ◽  
Author(s):  
John Avery
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Orbital Angular Momentum ◽  
Particle System ◽  
Total Spin ◽  
Particle Systems ◽  
Irreducible Representations ◽  
Angular Momentum Operator ◽  
Total Orbital Angular Momentum ◽  
Orbital Angular Momentum Operator

Methods are presented for constructing eigenfunctions of the total orbital angular momentum operator of a many-particle system without the use of the Clebsch–Gordan coefficients. One of the equations derived in this paper is analogous to Dirac's identity for total spin; and through this equation, a connection is established between eigenfunctions of L2 and irreducible representations of the symmetric group Sn.

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.

Optimal Design and Structural Precision Analysis for a Spherical Coordinate System 3D Scanner Guiding Device

2014 ◽  
Vol 705 ◽  
pp. 164-168
Author(s):  
Sang Wook Park ◽  
Hee Young Maeng ◽  
Ju Wook Park
Keyword(s):  
Optimal Design ◽  
Data Collection ◽  
Reverse Engineering ◽  
Coordinate System ◽  
Fem Analysis ◽  
Spherical Coordinate System ◽  
3D Scanner ◽  
Spherical Coordinate ◽  
Overall Performance ◽  
Improved Design

Recently, automatic 3D scanning devices are commonly researched and developed for better productivity of the reverse engineering fields. In this paper, a 3D scanner utilizing a spherical coordinate system was designed and analyzed using FEM analysis. The system was designed for optimal performance, high precision, minimal deflection, and speed of data collection. FEM analysis allowed us to properly design the system to achieve these goals, with focus on the deflection of the cantilever arm. Results of the FEM analysis and figures showing the apparatus design are provided. Successive prototypes are shown to increase in overall performance and reliability through improved design and analysis.

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