Symplectic integration of constrained hamiltonian systems

Mathematics of Computation

Volumn 63, Issue 208, 1994, Pages 589-605

  Leimkuhler, B ^a   Reich, S ^b  

^a UNIVERSITY OF KANSAS   (United States)

^b Institute of Applied Mathematics and Statistics ^*  (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968499113     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1994-1250772-7     Document Type: Article

References (20)

1. R. Abraham and J. E. Marsden, Foundations of mechanics, 2nd ed., Benjamin, Reading, MA, 1978.
2. V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., Vol. 60, Springer-Verlag, New York, 1975.
3. U. M. Ascher and L. R. Petzold, Stability of computational methods for constrained dynamics systems, SIAM J. Sci. Statist. Comput. 14 (1993), 95-120.
4. J. Baumgarte, Stabilization of constraints and integrals of motion in dynamical systems, Comp. Methods Appi. Mech. Engrg. 1 (1976), 1-16.
5. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical solution of initial value problems in differential-algebraic equations, North-Holland, Amsterdam, 1989.
6. G. J. Cooper, Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal. 7 (1987), 1-13.
7. R. Courant and D. Hilbert, Methods of mathematical physics, Wiley, New York, 1953.
8. P. A. M. Dirac, Lectures on quantum mechanics, Belfer Graduate School Monographs, no. 3, Yeshiva University, 1964.
9. E. Eich, C. Führer, B. Leimkuhler, and S. Reich, Stabilization and projection methods for multibody dynamics, Report A281, Helsinki Univ. of Technology, Helsinki, 1990.
10. L. Jay, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, Technical Report, Université de Genève, 1993.
11. B. Leimkuhler and S. Reich, Numerical methods for constrained Hamiltonian systems, Technical Report, Konrad Zuse Center, Berlin, 1992.
12. B. Leimkuhler and R. D. Skeel, Symplectic numerical integrators for constrained molecular dynamics, Technical Report, Dept, of Math., University of Kansas, Lawrence KS, 1992.
13. N. H. McClamroch and A. M. Bloch, Control of constrained Hamiltonian systems and applications to control of constrained robots, Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits (Fathi M. A. Salam and Mark L. Levi, eds.), SIAM, Philadelphia, PA, 1988, pp. 344-403.
14. T. Mrziglod, Zur Theorie und numerischen Realisierung von Lösungsmethoden bei Differentialgleichungen mit angekoppelten algebraischen Gleichungen, Diplomarbeit, Math. Inst., Univ. zu Köln, 1987.
15. J. M. Sanz-Sema, Symplectic integrators for Hamiltonian problems: an overview, Acta Numer. 1 (1991).
16. P. Olver, Applications of Lie groups to differential equations, Springer-Verlag, Berlin and New York, 1986.
17. F. Potra and W. Rheinboldt, On the numerical solution of the Euler-Lagrange equations, NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation (R. Deyo and E. Haug, eds.), Springer-Verlag, Berlin and New York, 1990.
18. S. Reich, Symplectic integration of constrained Hamiltonian systems by Runge-Kutta methods, Technical Report 93-13, Dept, of Comput. Sei., University of British Columbia, 1993.
19. W. Rheinboldt, Numerical analysis of parametrized nonlinear equations, Univ. Ark. Lecture Notes in Math. Sei., vol. 7, Wiley, New York, 1986.
20. J. M. Sanz-Sema, Runge-Kutta schemes for Hamiltonian systems, BIT 28 (1988), 877-883.