Position versus momentum projections for constrained Hamiltonian systems

Numerical Algorithms

Volumn 19, Issue 1-4, 1998, Pages 223-234

  Seiler, Werner M ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

Canonical transformation; Constrained dynamics; Dirac bracket; Hamiltonian system; Numerical integration; Orthogonal projection; Perturbed state space form

Indexed keywords

EID: 0032280464     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019170926730     Document Type: Article

References (16)

1. T. Alishenas, Zur numerischen Behandlung, Stabilisierung durch Projektion und Modellierung mechanischer Systeme mit Nebenbedingungen und Invarianten, Ph.D. thesis, Dept. of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, Sweden (1992).
2. T. Alishenas and Ö. Ólafsson, Modeling and velocity stabilization of constrained mechanical systems, BIT 34 (1994) 455-483.
3. V. Brasey and E. Hairer, Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, SIAM J. Numer. Anal. 30 (1993) 538-552.
4. V. Brasey and E. Hairer, Symmetrized half-explicit methods for constrained mechanical systems, Appl. Numer. Math. 13 (1993) 23-31.
5. H. Brauchli, Mass-orthogonal formulation of equations of motion for multibody systems, Z. Angew. Math. Phys. 42 (1991) 169-182.
6. C. Carathéodory, Variationsrechnung und Partielle Differentialgleichungen erster Ordnung, Band I (Teubner, Leipzig, 1956).
7. E. Eich, C. Führer, B. Leimkuhler and S. Reich, Stabilization and projection methods for multibody dynamics, Research Report A281, Helsinki University of Technology, Institute of Mathematics (1990).
8. H. Goldstein, Classical Mechanics (Addison-Wesley, New York, 1980).
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Springer Series in Computational Mathematics 14 (Springer, Berlin, 1996).
10. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton Univ. Press, 1992).
11. B.J. Leimkuhler and S. Reich, Symplectic integration of constrained Hamiltonian systems, Math. Comput. 63 (1994) 589-605.
12. S. Reich, Symplectic integration of constrained Hamiltonian systems by composition methods, SIAM J. Numer. Anal. 33 (1996) 475-491.
13. W.M. Seiler, Impetus-striction formalism and the numerical integration of constrained Hamiltonian systems (1998), in preparation.
14. W.M. Seiler, Numerical integration of constrained Hamiltonian systems using Dirac brackets, Math. Comput. (1998), to appear.
15. B. Simeon, MBSPACK - numerical integration software for constrained mechanical motion, Surv. Math. Ind. 5 (1995) 169-202.
16. M. Sofer, O. Melliger and H. Brauchli, Numerical behaviour of different formulations for multi-body dynamics, in: Numerical Methods in Engineering '92, eds. C. Hirsch, O.C. Zienkiewicz and E. Oñate (Elsevier, Amsterdam, 1992) pp. 277-284.