Basic Differential Geometry for Mechanics and Control
Differential geometry is an old mathematical discipline which contributed and contributes a lot to mathematical physics. Also its use in mechanics, electrodynamics or thermodynamics has a long history. Nevertheless, the introduction of the geometric methods to nonlinear, model based control occurred only about 25 years ago. The driving force for this development was the same as for physics, that is, geometric methods allow us to deal with dynamic systems in a coordinate free manner. Therefore, this contribution presents an overview on this discipline which starts with smooth manifolds, bundles, vector fields and finishes with jet bundles and jet coordinates.
KeywordsSmooth Manifold Infinitesimal Generator Integral Manifold Coordinate Chart Tangent Vector Field
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