Manifolds, Vectorfields, Lie Brackets, Distributions

  • Henk Nijmeijer
  • Arjan van der Schaft


In the previous chapter we have seen that many nonlinear control systems.


Tangent Space Coordinate Transformation Smooth Manifold Integral Manifold Nonlinear Control System 
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.


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  1. [AM78]
    R.A. Abraham and J.E. Marsden. Foundations of Mechanics. Benjamin/Cummings, Reading, 1978.Google Scholar
  2. [BJ73]
    T. Bröcker and K. Jänich. Einführung in die Differentialtopologie. Springer, Berlin, 1973.Google Scholar
  3. [Boo75]
    W.A. Boothby. An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, 1975.Google Scholar
  4. [Her62]
    R. Hermann. The differential geometry of foliations. J. Math. and Mech., 11:302–306, 1962.Google Scholar
  5. [Isi85]
    A. Isidori. Nonlinear Control Systems: An Introduction, volume 72 of Lect. Notes Contr. Inf. Sci. Springer-Verlag, Berlin, 1985.Google Scholar
  6. [Nag66]
    T. Nagano. Linear differential systems with singularities and applications to transitive Lie algebras. J. Math. Soc. Japan, 18:398–404, 1966.Google Scholar
  7. [Spi70]
    M. Spivak. A comprehensive introduction to differential geometry, Vol I. Publish or Perish, Boston, 1970.Google Scholar
  8. [Sus73]
    H. Sussmann. Orbits of families of vectorfields and integrability of distributions. Trans. Amer. Math. Soc., 180:171–188, 1973.Google Scholar
  9. [War70]
    F.W. Warner. Foundations of differentiable manifolds and Lie groups. Scott, Foresman, Glenview, 1970.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990, Corrected printing 2016 1990

Authors and Affiliations

  1. 1.Dynamics and Control GroupEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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