4.5 General Similarity Transformations

4.5.1 Similarity Transformations of Contact Regions

The following condition has to be fulfilled for the contact problem to be self-similar: the contact region for one value of the external parameter has to be geometrically similar to the contact region for any other admissible value of the parameter. It is well known from mathematics (group theory) that any similarity transformation on a plane can be decomposed into four transformations: (1) shifting; (2) rotation; (3) dilation of coordinates; and (4) mirror symmetry. The reduction of variables using the Π theorem and reduction of variables using the property of quasi-homogeneous functions are possible if the dilation transformation of variables is ...

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