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Volumn 68, Issue 226, 1999, Pages 661-681

Numerical integration of constrained Hamiltonian systems using Dirac brackets

Author keywords

Constrained Hamiltonian system; Dirac bracket; Extended Hamiltonian; Hamiltonian Dirac equations of motion; Numerical integration

Indexed keywords


EID: 0033426691     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01010-8     Document Type: Article
Times cited : (17)

References (31)
  • 1
    • 48749148224 scopus 로고
    • Rattle - A velocity version of the Shake algorithm for molecular dynamics calculations
    • H.C. Andersen, Rattle - a velocity version of the Shake algorithm for molecular dynamics calculations, J. Comp. Phys. 52 (1983), 24-34.
    • (1983) J. Comp. Phys. , vol.52 , pp. 24-34
    • Andersen, H.C.1
  • 2
    • 0003319234 scopus 로고
    • Mathematical methods of classical mechanics
    • Springer-Verlag, New York, MR 57:14033b
    • V.I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Mathematics 60, Springer-Verlag, New York, 1978. MR 57:14033b
    • (1978) Graduate Texts in Mathematics , vol.60
    • Arnold, V.I.1
  • 3
    • 21344492077 scopus 로고
    • Stabilization of DAEs and invariant manifolds
    • MR 94m:65121
    • U.M. Ascher, H. Chin, and S. Reich, Stabilization of DAEs and invariant manifolds, Num. Math. 67 (1994), 131-149. MR 94m:65121
    • (1994) Num. Math. , vol.67 , pp. 131-149
    • Ascher, U.M.1    Chin, H.2    Reich, S.3
  • 4
    • 34249680550 scopus 로고
    • Stabilization of constraints and integrals of motion in dynamical systems
    • MR 52:12448
    • J. Baumgarte, Stabilization of constraints and integrals of motion in dynamical systems, Comp. Meth. Appl. Mech. Eng. 1 (1972), 1-16. MR 52:12448
    • (1972) Comp. Meth. Appl. Mech. Eng. , vol.1 , pp. 1-16
    • Baumgarte, J.1
  • 5
    • 0003259286 scopus 로고    scopus 로고
    • Numerical solution of initial-value problems in differential-algebraic equations
    • SIAM, Philadelphia, MR 96h:65083
    • K.E. Brenan, S.L. Campbell, and L.R. Petzold, Numerical solution of initial-value problems in differential-algebraic equations, Classics in Applied Mathematics 14, SIAM, Philadelphia, 1996. MR 96h:65083
    • (1996) Classics in Applied Mathematics , vol.14
    • Brenan, K.E.1    Campbell, S.L.2    Petzold, L.R.3
  • 6
    • 0002211850 scopus 로고
    • Stability of Runge-Kutta methods for trajectory problems
    • MR 90d:65133
    • G.J. Cooper, Stability of Runge-Kutta methods for trajectory problems, IMA J. Num. Anal. 7 (1987), 1-13. MR 90d:65133
    • (1987) IMA J. Num. Anal. , vol.7 , pp. 1-13
    • Cooper, G.J.1
  • 7
    • 0030298714 scopus 로고    scopus 로고
    • Hamiltonian dynamics of an elastica and the stability of solitary waves
    • MR 97m:58072
    • D.J. Dichmann, J.H. Maddocks, and R.L. Pego, Hamiltonian dynamics of an elastica and the stability of solitary waves, Arch. Rat. Mech. Anal. 135 (1996), 357-396. MR 97m:58072
    • (1996) Arch. Rat. Mech. Anal. , vol.135 , pp. 357-396
    • Dichmann, D.J.1    Maddocks, J.H.2    Pego, R.L.3
  • 8
    • 0000115661 scopus 로고
    • Generalized Hamiltonian dynamics
    • MR 13:306b
    • P.A.M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2 (1950), 129-148. MR 13:306b
    • (1950) Can. J. Math. , vol.2 , pp. 129-148
    • Dirac, P.A.M.1
  • 9
    • 0000009882 scopus 로고
    • Generalized Hamiltonian dynamics
    • MR 20:724
    • _, Generalized Hamiltonian dynamics, Proc. Roy. Soc. A 246 (1958), 326-332. MR 20:724
    • (1958) Proc. Roy. Soc. A , vol.246 , pp. 326-332
  • 10
    • 0000022238 scopus 로고
    • Topological (Chern-Simons) quantum mechanics
    • MR 90m:81031
    • G.V. Dunne, R. Jackiw, and C.A. Trugenberger, Topological (Chern-Simons) quantum mechanics, Phys. Rev. D 41 (1990), 661-666. MR 90m:81031
    • (1990) Phys. Rev. D , vol.41 , pp. 661-666
    • Dunne, G.V.1    Jackiw, R.2    Trugenberger, C.A.3
  • 11
    • 0003437218 scopus 로고
    • Addison-Wesley, New York, MR 81j:70001
    • H. Goldstein, Classical mechanics, Addison-Wesley, New York, 1980. MR 81j:70001
    • (1980) Classical Mechanics
    • Goldstein, H.1
  • 14
    • 0000545837 scopus 로고    scopus 로고
    • Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
    • MR 97e:65065
    • L.O. Jay, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, SIAM J. Numer. Anal. 33 (1996), 368-387. MR 97e:65065
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 368-387
    • Jay, L.O.1
  • 15
    • 84968499113 scopus 로고
    • Symplectic integration of constrained Hamiltonian systems
    • MR 95b:65082
    • B.J. Leimkuhler and S. Reich, Symplectic integration of constrained Hamiltonian systems, Math. Comp. 63 (1994), 589-605. MR 95b:65082
    • (1994) Math. Comp. , vol.63 , pp. 589-605
    • Leimkuhler, B.J.1    Reich, S.2
  • 16
    • 0000408065 scopus 로고
    • Symplectic numerical integrators in constrained Hamiltonian systems
    • MR 95h:58053
    • B.J. Leimkuhler and R.D. Skeel, Symplectic numerical integrators in constrained Hamiltonian systems, J. Comp. Phys. 112 (1994), 117-125. MR 95h:58053
    • (1994) J. Comp. Phys. , vol.112 , pp. 117-125
    • Leimkuhler, B.J.1    Skeel, R.D.2
  • 17
    • 0040228678 scopus 로고
    • Stability of equilibria of Hamiltonian systems
    • (S. Sarkar, ed.), Hilger, Bristol, MR 87j:58063
    • R.S. MacKay, Stability of equilibria of Hamiltonian systems, Nonlinear Phenomena and Chaos (S. Sarkar, ed.), Hilger, Bristol, 1986, pp. 254-270. MR 87j:58063
    • (1986) Nonlinear Phenomena and Chaos , pp. 254-270
    • MacKay, R.S.1
  • 18
    • 21844498358 scopus 로고
    • An unconstrained Hamiltonian formulation for incompressible fluid flow
    • MR 96a:76085
    • J.H. Maddocks and R.L. Pego, An unconstrained Hamiltonian formulation for incompressible fluid flow, Comm. Math. Phys. 170 (1995), 207-217. MR 96a:76085
    • (1995) Comm. Math. Phys. , vol.170 , pp. 207-217
    • Maddocks, J.H.1    Pego, R.L.2
  • 21
    • 0042804677 scopus 로고    scopus 로고
    • Discrete gradient methods for solving ODEs numerically while preserving a first integral
    • MR 97e:65028
    • G.R.W. Quispel and G.S. Turner, Discrete gradient methods for solving ODEs numerically while preserving a first integral, J. Phys. A 29 (1996), L341-L349. MR 97e:65028
    • (1996) J. Phys. A , vol.29
    • Quispel, G.R.W.1    Turner, G.S.2
  • 22
    • 0001558971 scopus 로고    scopus 로고
    • Symplectic integration of constrained Hamiltonian systems by composition methods
    • MR 97h:65103
    • S. Reich, Symplectic integration of constrained Hamiltonian systems by composition methods, SIAM J. Num. Anal. 33 (1996), 475-491. MR 97h:65103
    • (1996) SIAM J. Num. Anal. , vol.33 , pp. 475-491
    • Reich, S.1
  • 23
    • 84972474778 scopus 로고
    • Semigeostrophic theory as a Dirac-bracket projection
    • MR 90j:76097
    • R. Salmon, Semigeostrophic theory as a Dirac-bracket projection, J. Fluid Mech. 196 (1988), 345-358. MR 90j:76097
    • (1988) J. Fluid Mech. , vol.196 , pp. 345-358
    • Salmon, R.1
  • 25
    • 21844527049 scopus 로고
    • Involution and constrained dynamics II: The Faddeev-Jackiw approach
    • MR 97h:70018
    • W.M. Seiler, Involution and constrained dynamics II: The Faddeev-Jackiw approach, J. Phys. A 28 (1995), 7315-7331. MR 97h:70018
    • (1995) J. Phys. A , vol.28 , pp. 7315-7331
    • Seiler, W.M.1
  • 26
    • 0039044718 scopus 로고    scopus 로고
    • Momentum versus position projections for constrained Hamiltonian systems
    • submitted
    • _, Momentum versus position projections for constrained Hamiltonian systems, Num. Algo., submitted.
    • Num. Algo.
  • 27
    • 0032024775 scopus 로고    scopus 로고
    • Numerical analysis of constrained Hamiltonian systems and the formal theory of differential equations
    • _, Numerical analysis of constrained Hamiltonian systems and the formal theory of differential equations, Math. Comp. Simul. 45 (1998), 561-576.
    • (1998) Math. Comp. Simul. , vol.45 , pp. 561-576
  • 28
    • 21844481183 scopus 로고
    • Involution and constrained dynamics I: The Dirac approach
    • MR 97f:70024
    • W.M. Seiler and R.W. Tucker, Involution and constrained dynamics I: The Dirac approach, J. Phys. A 28 (1995), 4431-4451. MR 97f:70024
    • (1995) J. Phys. A , vol.28 , pp. 4431-4451
    • Seiler, W.M.1    Tucker, R.W.2
  • 30
    • 0000867592 scopus 로고
    • Dirac brackets in geometric dynamics
    • MR 50:11319
    • J. Śniatycki, Dirac brackets in geometric dynamics, Ann. Inst. Henri Poincaré A 20 (1974), 365-372. MR 50:11319
    • (1974) Ann. Inst. Henri Poincaré A , vol.20 , pp. 365-372
    • Śniatycki, J.1
  • 31
    • 0003306954 scopus 로고
    • Constrained dynamics
    • Springer-Verlag, New York, MR 84f:58051
    • K. Sundermeyer, Constrained dynamics, Lecture Notes in Physics 169, Springer-Verlag, New York, 1982. MR 84f:58051
    • (1982) Lecture Notes in Physics , vol.169
    • Sundermeyer, K.1


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