scholarly journals Direct Integration Methods of the N-Body Problem

1971 ◽  
Vol 10 ◽  
pp. 118-132 ◽  
Author(s):  
S. J. Aarseth
Keyword(s):  
Body Problem ◽  
Computational Algorithm ◽  
Close Binaries ◽  
Polynomial Method ◽  
Time Step ◽  
Simple Method ◽  
Regularization Procedure ◽  
N Body Problem ◽  
Order Polynomial ◽  
Fourth Order Polynomial

AbstractA fourth-order polynomial method for the integration of N-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual time-step scheme but the calculation of close encounters and persistent binary orbits is rather time-consuming and is best performed by special techniques. A discussion is given of the Kustaanheimo-Stiefel regularization procedure which is used to integrate dominant two-body encounters as well as close binaries. Suitable decision-making parameters are introduced and a simple method is developed for regularizing an arbitrary number of simultaneous two-body encounters.

Estimation of fabric opacity by scanner

Sensor Review ◽  
2014 ◽  
Vol 34 (4) ◽  
pp. 404-409
Author(s):  
Abbas Hajipour ◽  
Ali Shams Nateri ◽  
Alireza Sadr Momtaz
Keyword(s):  
Textile Industry ◽  
Polynomial Regression ◽  
Low Cost ◽  
Color Space ◽  
Simple Method ◽  
Content Type ◽  
Textile Fabrics ◽  
Order Polynomial ◽  
Textile Fabric ◽  
Fourth Order Polynomial

Purpose – This study aimed to use a scanner as a low-cost method for measuring the opacity of textile fabric. Textile fabrics must have specific ranges of opacity according to their uses for shirting, curtaining, etc. In this way, opacity is an important property in the textile industry. Conventionally, textile opacity is estimated using a spectrophotometer, which is an expensive method. Design/methodology/approach – In this study a scanner was used as a low-cost method for measuring the opacity of textile fabric. The opacity was estimated by using red, green and blue (RGB) parameters of images of fabric against white and black background. Findings – The accuracy of opacity estimation was improved by converting RGB into several color spaces. The best opacity estimation was obtained by using the XYZ color space. In addition, using a regression method, the best estimation was obtained by using a fourth-order polynomial regression with the LSLM color space. Originality/value – The opacity of fabric has been measured by spectrophotometer, but in this study, the opacity of fabric was measured by scanner as a low cost device and also with novel and simple method. This method achieved acceptable accuracy for opacity estimation. The obtained result is comparable with spectrophotometer results.

scholarly journals On frequency estimations in phase fitted variational integrators for the general N-body problem

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 33-34
Author(s):  
Odysseas Kosmas ◽  
Sigrid Leyendecker
Keyword(s):  
Body Problem ◽  
Variational Integrators ◽  
N Body Problem

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

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