Curvilinear

Curvilinear

Heat Conduction

Published in Greg F. Naterer, Advanced Heat Transfer, 2018

In the previous section, standard coordinate systems including Cartesian and radial coordinates were presented. For more complex geometrical configurations, curvilinear coordinates may be used. Curvilinear coordinates refer to a coordinate system in which the coordinate lines may be curved. The coordinates can be obtained by a mapping from Cartesian coordinates by a coordinate transformation that is locally invertible (a one-to-one mapping from any point in the Cartesian coordinates to curvilinear coordinates). Common examples of curvilinear coordinate systems include cylindrical and spherical coordinates. These coordinates are illustrated in Figure 2.10. Other examples include ellipsoidal, toroidal, bispherical, and oblate spheroidal coordinates. Ellipsoidal coordinates are the most generalized coordinate system from which other curvilinear coordinate systems are special cases.

Detailed wheel/rail geometry processing using the planar contact approach

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Journal Information

Published in Vehicle System Dynamics, 2022

E. A. H. Vollebregt

Design choices are to restrict attention to 3-dimensional space, using right-handed coordinate systems and as the unit of length where possible. Cartesian coordinates, cylindrical coordinates and (generalised) curvilinear coordinates are used. Left-handed coordinates are needed sometimes when using mirroring between left and right wheels, to consider both sides with a single software implementation. A vector (3-vector) is a triplet associated with the three coordinate axes of a coordinate system: .

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Heat Conduction

Detailed wheel/rail geometry processing using the planar contact approach