Two and Three Dimensional Calculus by Phil Dyke

Author:Phil Dyke [Dyke, Phil]
Language: eng
Format: epub
ISBN: 9781119221807
Publisher: Wiley
Published: 2018-02-26T00:00:00+00:00

will be a tangent to this curve in the local (osculating) plane that contains the curve. This enables the scale factors and to be defined as follows:

The scale factors are not simply local radii of curvature, but the ratio of the infinitesimal length of divided by the change in the direction of the three co-ordinates taken in turn. It is possible using the language of manifolds and tangent bundles to put all this far more rigorously, but this would be out of place here. Our three scale factors turn out to be the diagonal elements of a matrix or second-order tensor that is only diagonal for orthogonal curvilinear co-ordinate systems. As attention is actually restricted to these orthogonal systems here, such excursions into generality would be an unnecessary complication. Hence, the scale factors appear simply as ratios of infinitesimals; they do not have a consistent dimension though to consider them as lengths related to radius of curvature might be useful for the polar examples encountered later. Here, we have

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.