In railroad vehicle dynamics, Euler angles are often used to describe the track geometry (track centerline and rail space curves). The tangent and curvature vectors as well as local geometric properties such as the curvature and torsion can be expressed in terms of Euler angles. Some of the local geometric properties and Euler angles can be related to measured parameters that are often used to define the track geometry. The Euler angles employed, however, define a coordinate system that may differ from the Frenet frame used in the classical differential geometry. The relationship between the track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves is developed in this paper and is used to shed light on some of the formulas and identities used in the geometric description in railroad vehicle dynamics. The conditions under which the two frames (track and Frenet) become equivalent are presented and used to obtain expressions for the curvature and torsion in terms of Euler angles and their derivatives with respect to the arc length.
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July 2006
Technical Briefs
Rail Geometry and Euler Angles
Cheta Rathod,
Cheta Rathod
Department of Mechanical Engineering,
University of Illinois at Chicago
, 842 West Taylor Street, Chicago, IL 60607
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Ahmed A. Shabana
Ahmed A. Shabana
Department of Mechanical Engineering,
University of Illinois at Chicago
, 842 West Taylor Street, Chicago, IL 60607
Search for other works by this author on:
Cheta Rathod
Department of Mechanical Engineering,
University of Illinois at Chicago
, 842 West Taylor Street, Chicago, IL 60607
Ahmed A. Shabana
Department of Mechanical Engineering,
University of Illinois at Chicago
, 842 West Taylor Street, Chicago, IL 60607J. Comput. Nonlinear Dynam. Jul 2006, 1(3): 264-268 (5 pages)
Published Online: March 9, 2006
Article history
Received:
November 21, 2005
Revised:
March 9, 2006
Citation
Rathod, C., and Shabana, A. A. (March 9, 2006). "Rail Geometry and Euler Angles." ASME. J. Comput. Nonlinear Dynam. July 2006; 1(3): 264–268. https://doi.org/10.1115/1.2198878
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