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: | , |
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Format: | Article |
Published: |
2002
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Online Access: | http://journalarticle.ukm.my/1388/ http://www.ukm.my/jkukm/index.php/jkukm |
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Summary: | 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 |
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