On representations and integrability of mathematical structures in energy-conserving physical systems

SIAM Journal on Control and Optimization

Volumn 37, Issue 1, 1999, Pages 54-91

  Dalsmo, Morten ^a   Van Der Schaft, Arjan ^b  

^a ABB CORPORATE RESEARCH   (Norway)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Actuated mechanical systems; Dirac structures; External variables; Hamiltonian systems; Implicit systems; Integrability; Interconnections; Kinematic constraints

Indexed keywords

CONSTRAINT THEORY; KINEMATICS; MATHEMATICAL MODELS; SYSTEM THEORY;

DIRAC STRUCTURES; HAMILTONIAN SYSTEMS; KINEMATIC CONSTRAINTS;

LARGE SCALE SYSTEMS;

EID: 0032154062     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012996312039     Document Type: Article

References (29)

1. V.I. ARNOLD, V.V. KOZLOV, AND A.I. NEISHTADT, Mathematical Aspects of Classical and Celestial Mechanics, Springer-Verlag, Berlin, New York, 1997.
2. R. ABRAHAM, J.E. MARSDEN, AND T. RATIU, Manifolds, Tensor Analysis, and Applications, Springer-Verlag, Berlin, New York, 1988.
3. A.M. BLOCH AND P.E. CROUCH, Nonholonomic control systems on Riemannian manifolds, SIAM J. Control Optim., 33 (1995), pp. 126-148.
4. A.M. BLOCK, P.S. KRISHNAPRASAD, J.E. MARSDEN, AND R.M. MURRAY, Nonholonomic mechanical systems with symmetry, Arch. Rational Mech. Anal., 136 (1996), pp. 21-99.
5. T.J. COURANT, Dirac manifolds, Trans. Amer. Math. Soc., 319 (1990), pp. 631-661.
6. P.E. CROUCH, Handwritten notes, 1994.
7. T.J. COURANT AND A. WEINSTEIN, Beyond Poisson structures, in Seminaire sudrhodanien de geometrie 8, Travaux en Cours 27, Hermann, Paris, 1988.
8. I. DORFMAN, Dirac structures of integrable evolution equations, Phys. Lett. A, 125 (1987), pp. 240-246.
9. I. DORFMAN, Dirac Structures and Integrability of Nonlinear Evolution Equations, John Wiley, Chichester, 1993.
10. P. DIRAC, Generalized Hamiltonian dynamics, Canad. J. Math., 2 (1950), pp. 129-148.
11. D.L. JONES AND F. J. EVANS, Variational analysis of electrical networks, J. Franklin Inst., 295 (1973), pp. 9-23.
12. A.G.J. MACFARLANE, An integral formulation of a canonical equation set for non-linear electrical networks, Internat. J. Control, 11 (1970), pp. 449-470.
13. B.M. MASCHKE, Elements on the modelling of multibody systems, in Modelling and Control of Mechanisms and Robot Systems, C. Melchiorri and A. Tornambe, eds., World Scientific Publishing Ltd., River Edge, NJ, 1996, pp. 1-38.
14. B.M. MASCHKE, C. BIDARD, AND A.J. VAN DER SCHAFT, Screw-vector bond graphs for the kinestatic and dynamic modeling of multibody systems, Dynamic Systems and Control, 55(1994), pp. 637-644.
15. J.E. MARSDEN AND T. RATIU, Introduction to Mechanics and Symmetry, Springer-Verlag, Berlin, New York, 1994.
16. B.M. MASCHKE AND A.J. VAN DER SCHAFT, Port-controlled Hamiltonian systems: Modelling origins and system theoretic properties, in Proc. IFAC Symp. NOLCOS, Bordeaux, France, 1992, M. Fliess, ed., International Federation of Automatic Control, pp. 282-288.
17. B.M. MASCHKE AND A.J. VAN DER SCHAFT, System-theoretic properties of port-controlled Hamiltonian systems, in Systems and Networks: Mathematical Theory and Applications, vol. II, Akademie Verlag, Berlin, 1994, pp. 349-352.
18. B.M. MASCHKE AND A.J. VAN DER SCHAFT, A Hamiltonian approach to stabilization of nonholonomic mechanical systems, in Proc. 33rd IEEE CDC, Orlando, FL, 1994, IEEE Control Systems Society, pp. 2950-2954.
19. B.M. MASCHKE, A.J. VAN DER SCHAFT, AND P.C. BREEDVELD, An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators, J. Franklin Inst., 329 (1992), pp. 923-966.
20. B.M. MASCHKE, A.J. VAN DER SCHAFT, AND P.C. BREEDVELD, An intrinsic Hamiltonian formulation of the dynamics of LC-circuits, IEEE Trans. Circuits Systems I Fund. Theory Appl., 42 (1995), pp. 73-82.
21. H. NIJMEIJER AND A.J. VAN DER SCHAFT, Nonlinear Dynamical Control Systems, Springer-Verlag, Berlin, New York, 1990.
22. P.J. OLVER, Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, Berlin, New York, 1993.
23. R. ORTEGA AND M.W. SPONG, Adaptive motion control of rigid robots: A tutorial, Automatica J. IFAC, 25 (1989), pp. 877-888.
24. J.J. SLOTINE, Putting Physics in Control: The Example of Robotics, IEEE Control Systems Mag., 8 (1988), pp. 12-18.
25. A. J. VAN DER SCHAFT AND B.M. MASCHKE, On the Hamiltonian formulation of non-holonomic mechanical systems. Rep. Math. Phys., 34 (1994), pp. 225-233.
26. A.J. VAN DER SCHAFT AND B.M. MASCHKE, The Hamiltonian formulation of energy conserving physical systems with external ports, Arch, für Elektronik und Übertragungstechnik, 49 (1995), pp. 362-371.
27. A.J. VAN DER SCHAFT AND B.M. MASCHKE, Mathematical modelling of constrained Hamiltonian systems, in Proc. IFAC Symp. NOLCOS, Tahoe City, CA, 1995, International Federation of Automatic Control, pp. 678-683.
28. M. TAKEGAKI AND S. ARIMOTO, A new feedback method for dynamic control of manipulators, Trans. ASME J. Dynam. System Meas. Control, 103 (1981), pp. 119-125.
29. A. WEINSTEIN, The local structure of Poisson manifolds, J. Differential Geom., 18 (1983), pp. 523-557.