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TECHNICAL BRIEF

Rail Geometry and Euler Angles

[+] Author and Article Information
Cheta Rathod, Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS . Manuscript received November 21, 2005; final manuscript received March 9, 2006. Review conducted by John J. McPhee.

J. Comput. Nonlinear Dynam 1(3), 264-268 (Mar 09, 2006) (5 pages) doi:10.1115/1.2198878 History: Received November 21, 2005; Revised March 09, 2006

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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Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Sequence of Euler angles and Frenet frame

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