An Introduction To Controllability Using Forms

by Kevin Davis


This paper serves as a brief overview into determining controllability using forms, using the concept of the derived flag. It is not original work done by me, but it is an attempt to present the material from (cite source) in terms that someone not intimately familiar with differential geometry or exterior differential systems can understand clearly. The example of a penny rolling on a plane will be used to demonstrate the method of determining controllability using forms, as well as to show the similarities between the forms method and the more common method of using vector fields (the Lie Bracket method). There will also be a brief review of controllability using Lie Brackets, to make sure that everyone is up to speed with both methods.

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