Basic Differential Geometry for Mechanics and Control

  • Kurt Schlacher
  • Kurt Zehetleitner
Part of the International Centre for Mechanical Sciences book series (CISM, volume 444)


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.


Smooth Manifold Infinitesimal Generator Integral Manifold Coordinate Chart Tangent Vector Field 
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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Kurt Schlacher
    • 1
  • Kurt Zehetleitner
    • 1
  1. 1.Institute of Automatic Control and Control Systems TechnologyJohannes Kepler University of LinzAustria

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