Advertisement

Basic Differential Geometry for Mechanics and Control

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

Abstract

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.

Keywords

Smooth Manifold Infinitesimal Generator Integral Manifold Coordinate Chart Tangent Vector Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. W. M. Boothby. An Introduction to Differentiable Manifolds and Riemanmnian Geometry. Academic Press, Inc., Orlando, USA, 1986.Google Scholar
  2. Y. Choquet-Bruhat and C. DEWitt-Morette. Analysis, Manifolds and Physics. North Holland, Amsterdam, 1982.MATHGoogle Scholar
  3. Th. Frankel. The Geometry of Physics, An Introduction. Cambridge University Press, Cambridge, UK, 1998.Google Scholar
  4. P. J. Olver. Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge, UK, 1995.CrossRefMATHGoogle Scholar
  5. J. F. Pommaret. Systems of Partial Differential Equations and Lie Pseudogroups. Gordon and Breach Science Publishers, New York, USA, 1978.Google Scholar
  6. D. J. Saunders. The Geometry of Jet Bundles. Cambridge University Press, Cambridge, UK, 1989.CrossRefMATHGoogle Scholar
  7. M. Spivak. Differential Geometry, Vol. 1 to 5. Publish or Perish, Inc., Houston, Texas, 1979.Google Scholar
  8. K. Zehetleitner and K. Schlacher. Computer algebra methods for implicit dynamic systems and applications. Mathematics and Computers in Simulation,to appear, ‘2003.Google Scholar

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

Personalised recommendations