General algorithms for 3-D motion of a non-planar body in a steady-state force field

Determining trajectories of objects in three-dimensional space is fundamental to many disciplines. Whether the objects be molecules or celestial bodies, the standard Newtonian equations of motion describe this dynamic behavior. Unfortunately, however the complexity of a real system normally requi...

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Main Authors:	M.Pratt, Ronald, Khairil Mazwan Mohamad Zaini
Format:	Article
Published:	2002
Online Access:	http://journalarticle.ukm.my/1388/ http://journalarticle.ukm.my/1388/

id	ukm-1388
recordtype	eprints
spelling	ukm-13882011-10-11T03:45:29Z http://journalarticle.ukm.my/1388/ General algorithms for 3-D motion of a non-planar body in a steady-state force field M.Pratt, Ronald Khairil Mazwan Mohamad Zaini, Determining trajectories of objects in three-dimensional space is fundamental to many disciplines. Whether the objects be molecules or celestial bodies, the standard Newtonian equations of motion describe this dynamic behavior. Unfortunately, however the complexity of a real system normally requires that the equations of motion be solved numerically and methods presented in classical mechanics textbooks are of little practical use. In addition, the standard equations of motion involving Eulaer angles contain singularities and are therefore not suitable for computer solution. This paper discusses implementation of two powerful but little known techniques using quaternions, the Evans and the Rapaport methods. These little known techniques have been developed by and used for molecular modeling, but their application is far reaching, and can be applied to any system where quantum or relativistic effects may be neglected. These methods shoe excellent conservation of energy over many millions of time steps and are free of singularities. Herein we compare the two methods in terms of efficiency and accuracy. Due to their general nature, the algorithms may be readily coded to meet the needs of many applications 2002 Article PeerReviewed M.Pratt, Ronald and Khairil Mazwan Mohamad Zaini, (2002) General algorithms for 3-D motion of a non-planar body in a steady-state force field. Jurnal Kejuruteraan, 14 . http://www.ukm.my/jkukm/index.php/jkukm
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
description	Determining trajectories of objects in three-dimensional space is fundamental to many disciplines. Whether the objects be molecules or celestial bodies, the standard Newtonian equations of motion describe this dynamic behavior. Unfortunately, however the complexity of a real system normally requires that the equations of motion be solved numerically and methods presented in classical mechanics textbooks are of little practical use. In addition, the standard equations of motion involving Eulaer angles contain singularities and are therefore not suitable for computer solution. This paper discusses implementation of two powerful but little known techniques using quaternions, the Evans and the Rapaport methods. These little known techniques have been developed by and used for molecular modeling, but their application is far reaching, and can be applied to any system where quantum or relativistic effects may be neglected. These methods shoe excellent conservation of energy over many millions of time steps and are free of singularities. Herein we compare the two methods in terms of efficiency and accuracy. Due to their general nature, the algorithms may be readily coded to meet the needs of many applications
format	Article
author	M.Pratt, Ronald Khairil Mazwan Mohamad Zaini,
spellingShingle	M.Pratt, Ronald Khairil Mazwan Mohamad Zaini, General algorithms for 3-D motion of a non-planar body in a steady-state force field
author_facet	M.Pratt, Ronald Khairil Mazwan Mohamad Zaini,
author_sort	M.Pratt, Ronald
title	General algorithms for 3-D motion of a non-planar body in a steady-state force field
title_short	General algorithms for 3-D motion of a non-planar body in a steady-state force field
title_full	General algorithms for 3-D motion of a non-planar body in a steady-state force field
title_fullStr	General algorithms for 3-D motion of a non-planar body in a steady-state force field
title_full_unstemmed	General algorithms for 3-D motion of a non-planar body in a steady-state force field
title_sort	general algorithms for 3-d motion of a non-planar body in a steady-state force field
publishDate	2002
url	http://journalarticle.ukm.my/1388/ http://journalarticle.ukm.my/1388/
first_indexed	2023-09-18T19:33:11Z
last_indexed	2023-09-18T19:33:11Z
_version_	1777405097717792768

General algorithms for 3-D motion of a non-planar body in a steady-state force field

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