The Euler equation is a correct way for writing rotational moments of solids. But it is simple only if written in rotating frames. Applying it to railway wheelsets is difficult because it necessitates using the Euler angles, or Euler parameters, combined to rotation matrices or, numerically more stable, quaternions. Euler angles can be avoided in railway specific codes, by writing dynamical equations in track frames. However, academic literature [Landau LD, Lifshitz EM. Mechanics (Institute of Physical Problems, USSR Academy of Sciences, Moscow), Vol. 1, Course of theoretical physics. 21st English ed. Oxford (UK): Elsevier; 1960; Shabana AA, Zaazaa KE, Sugiyama H. Railroad vehicle dynamics. CRC Press; 2008.] does not provide simple solutions as to how properly writing equations of gyroscopic moments in no rotating frames. This paper describes how it is possible, owing to an approximation validated for railway applications, to avoid Euler angles and rotation matrices, while correctly taking into account gyroscopic effects. Using a most severe example, emphasising gyroscopic effects, it is demonstrated that a fast specific code using the approximation provides results equivalent to those of an multi body system generalised code with no approximation.
Rotational equations usable for railway wheelsets
Vehicle System Dynamics ; 52 , 3 ; 390-409
2014
20 Seiten, 13 Bilder, 10 Tabellen, 13 Quellen
Article (Journal)
English
Rotational equations usable for railway wheelsets
Online Contents | 2014
|Rotational equations usable for railway wheelsets
Automotive engineering | 2014
|Rotational equations usable for railway wheelsets
Taylor & Francis Verlag | 2014
|SAGE Publications | 1990
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