Original manuscript: 2017/05/15
Manuscript last revised: 2017/08/16
The areas of mechanics and control theory have a rich and productive history of interaction with the broad mathematical subject of differential geometry. An overview is given for these sorts of interplay in the areas of Riemannian and affine differential geometry, and the geometry of vector distributions. Emphasis is given to areas where differential geometric methods have played a crucial r\^ole in solving problems whose solution is difficult to achieve without access to these methods. The results overviewed, while forming a coherent and elegant body of work, are limited in scope. The paper is closed with a discussion of why the approach is limited, and a brief discussion of issues that must be resolved before the results of the type presented in the paper can be extended.
Last Updated: Mon Jul 30 07:47:15 2018