In railroad vehicle dynamics, the motion of vehicle components strongly depends on the wheel and rail geometries. It is important to recognize that Euler angles are used in this chapter for two fundamentally different purposes: as motion‐generalized coordinates to describe rigid body kinematics in space; and as geometry field variables to uniquely define the geometry of track and rail space curves. The chapter introduces a general form of transformation matrix that defines the orientation of the body in space and is used to define transformation matrices as a result of performing simple rotations about the axes of the body coordinate system. The body orientation can be defined using orientation parameters that define the direction cosines of the axes of the body coordinate system in the global coordinate system. To understand the mathematical foundations of some of the terminology used in track descriptions, the chapter discusses some basic geometry concepts, starting with the curvature vector.
Motion and Geometry Descriptions
2021-04-05
41 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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