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Articles

Modelling of piezoelectric structures–a Hamiltonian approach

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Pages 179-193 | Received 08 Feb 2007, Accepted 17 Aug 2007, Published online: 08 Apr 2008

References

  • van der Schaft , A. J. 2000 . L2-Gain and Passivity Techniques in Nonlinear Control , London : Springer .
  • Macchelli , A. 2002 . Port Hamiltonian Systems – A unified approach for modeling and control , Italy : University of Bologna . Ph.D. Thesis
  • van der Schaft , A. J. and Maschke , B. M. 2002 . Hamiltonian formulation of distributed-parameter systems with boundary energy flow . J. Geom. Phys. , 42 : 166 – 194 .
  • Ennsbrunner , H. and Schlacher , K. 2005 . On the geometrical representation and interconnection of infinite dimensional port controlled Hamiltonian systems . 44th IEEE, Conference on Decision and Control and European Control Conference . 2005 , Sevilla, Spain.
  • Olver , P. J. 1986 . Applications of Lie Groups to Differential Equations , New York : Springer .
  • Giachetta , G. , Sardanashvily , G. and Mangiarotti , L. 1994 . New Lagrangian and Hamiltonian Methods in Field Theory , New York : World Scientific .
  • Saunders , D. J. 1989 . The Geometry of Jet Bundles , Cambridge : Cambridge University Press .
  • Boothby , W. M. 1986 . An Introduction to Differentiable Manifolds and Riemanian Geometry , Orlando : Academic Press .
  • Pommaret , J. F. 1978 . Systems of Partial Differential Equations and Lie Pseudogroups , New York : Gordon and Breach .
  • Kugi , A. 2001 . Non-linear Control Based on Physical Models , London : Springer .
  • Macchelli , A. and Melchiorri , C. 2004 . Control by interconnection and energy shaping of the Timoshenko beam . J. Math. Comput. Model. Dynamical Syst. (MCMDS) , 10 : 231 – 251 .
  • Hebey , E. 2000 . Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities , New York : Courant Institute of Mathematical Sciences .
  • Zeidler , E. 1995 . Applied Functional Analysis , New York : Springer .

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