메뉴 건너뛰기




Volumn 53, Issue 2, 2004, Pages 211-260

Singular reduction of implicit Hamiltonian systems

Author keywords

Dirac structures; Implicit hamiltonian systems; Reduction; Symmetry

Indexed keywords


EID: 2942729971     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(04)90013-4     Document Type: Article
Times cited : (24)

References (43)
  • 3
    • 0002881562 scopus 로고
    • A universal reduction procedure for Hamiltonian group actions
    • T. Ratiu (ed.), Springer
    • J. Arms, R. Cushman and M. Gotay: A universal reduction procedure for Hamiltonian group actions. In T. Ratiu (ed.), The Geometry of Hamiltonian Systems, 33-51. Springer, 1991.
    • (1991) The Geometry of Hamiltonian Systems , pp. 33-51
    • Arms, J.1    Cushman, R.2    Gotay, M.3
  • 4
    • 0001541212 scopus 로고    scopus 로고
    • Proper group actions and symplectic stratified spaces
    • L. Bates and E. Lerman: Proper group actions and symplectic stratified spaces, Pacific J. Math. 181(2) (1997), 201-229.
    • (1997) Pacific J. Math. , vol.181 , Issue.2 , pp. 201-229
    • Bates, L.1    Lerman, E.2
  • 7
    • 0002540789 scopus 로고    scopus 로고
    • Symmetry and reduction in implicit generalized Hamiltonian systems
    • G. Blankenstein and A. J. van der Schaft: Symmetry and reduction in implicit generalized Hamiltonian systems, Rep. Math. Phys. 47 (2001), 57-100.
    • (2001) Rep. Math. Phys. , vol.47 , pp. 57-100
    • Blankenstein, G.1    van der Schaft, A.J.2
  • 8
    • 0001061853 scopus 로고    scopus 로고
    • Representations of Dirac structures on vector spaces and nonlinear L-C circuits
    • H. Hermes, G. Ferraya, R. Gardner, and H. Sussmann (eds.)
    • A. M. Bloch and P. E. Crouch: Representations of Dirac structures on vector spaces and nonlinear L-C circuits. In H. Hermes, G. Ferraya, R. Gardner, and H. Sussmann (eds.), Proc. Symp. Pure Math., Differential Geometry and Control Theory 64 (1999), 103-117.
    • (1999) Proc. Symp. Pure Math., Differential Geometry and Control Theory , vol.64 , pp. 103-117
    • Bloch, A.M.1    Crouch, P.E.2
  • 12
    • 0039789453 scopus 로고
    • On singular reduction of Hamiltonian spaces
    • P. Donato et al. (ed.), Birkhäuser, Boston
    • R. Cushman and R. Sjamaar: On singular reduction of Hamiltonian spaces. In P. Donato et al. (ed.), Symplectic Geometry and Mathematical Physics, pp. 114-128, Birkhäuser, Boston, 1991.
    • (1991) Symplectic Geometry and Mathematical Physics , pp. 114-128
    • Cushman, R.1    Sjamaar, R.2
  • 13
    • 0035622635 scopus 로고    scopus 로고
    • Differential structure of orbit spaces
    • R. Cushman and J. Śniatycki: Differential structure of orbit spaces, Canad. J. Math. 53 (2001), 715-755.
    • (2001) Canad. J. Math. , vol.53 , pp. 715-755
    • Cushman, R.1    Śniatycki, J.2
  • 14
    • 0032154062 scopus 로고    scopus 로고
    • On representations and integrability of mathematical structures in energy-conserving physical systems
    • M. Dalsmo and A. J. van der Schaft: On representations and integrability of mathematical structures in energy-conserving physical systems, SIAM J. Opt. Cont. 37 (1999), 54-91.
    • (1999) SIAM J. Opt. Cont. , vol.37 , pp. 54-91
    • Dalsmo, M.1    van der Schaft, A.J.2
  • 17
    • 0002631480 scopus 로고
    • On the construction of the reduced phase space of a Hamiltonian system with symmetry
    • M. Kummer: On the construction of the reduced phase space of a Hamiltonian system with symmetry, Indiana Univ. Math. J. 30 (1981), 281-291.
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 281-291
    • Kummer, M.1
  • 18
    • 0000388063 scopus 로고
    • Examples of singular reduction
    • D. A. Salamon (ed.), Cambridge University Press
    • E. Lerman, R. Montgomery and R. Sjamaar: Examples of singular reduction, In: Symplectic Geometry, D. A. Salamon (ed.), pp. 127-155, Cambridge University Press, 1993.
    • (1993) Symplectic Geometry , pp. 127-155
    • Lerman, E.1    Montgomery, R.2    Sjamaar, R.3
  • 20
    • 0032021284 scopus 로고    scopus 로고
    • Dirac structures and Poisson homogeneous spaces
    • Z.-J. Liu, A. Weinstein and P. Xu: Dirac structures and Poisson homogeneous spaces. Commun. Math. Phys. 192 (1998), 121-144.
    • (1998) Commun. Math. Phys. , vol.192 , pp. 121-144
    • Liu, Z.-J.1    Weinstein, A.2    Xu, P.3
  • 24
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • J. E. Marsden and A. Weinstein: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121-130.
    • (1974) Rep. Math. Phys. , vol.5 , pp. 121-130
    • Marsden, J.E.1    Weinstein, A.2
  • 25
    • 0003207640 scopus 로고    scopus 로고
    • Interconnected mechanical systems, part II: The dynamics of spatial mechanical networks
    • A. Astolfi, D. J. N. Limebeer, C. Melchiorri, A. Tornambè, and R. B. Vinter (eds.), Imperial College Press
    • B. M. Maschke and A. J. van der Schaft: Interconnected mechanical systems, part II: The dynamics of spatial mechanical networks, In A. Astolfi, D. J. N. Limebeer, C. Melchiorri, A. Tornambè, and R. B. Vinter (eds.), Modelling and Control of Mechanical Systems, pp. 17-30, Imperial College Press, 1997.
    • (1997) Modelling and Control of Mechanical Systems , pp. 17-30
    • Maschke, B.M.1    van der Schaft, A.J.2
  • 29
    • 0002083047 scopus 로고    scopus 로고
    • Singular reduction of Poisson manifolds
    • J.-P. Ortega and T. S. Ratiu: Singular reduction of Poisson manifolds, Lett. Math. Phys. 46 (1998), 359-372.
    • (1998) Lett. Math. Phys. , vol.46 , pp. 359-372
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 30
    • 8644228948 scopus 로고    scopus 로고
    • Momentum Maps and Hamiltonian Reduction
    • Birkhäuser, Boston
    • J.-P. Ortega and T. S. Ratiu: Momentum Maps and Hamiltonian Reduction, Progress in Mathematics 222, Birkhäuser, Boston 2003.
    • (2003) Progress in Mathematics , vol.222
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 31
    • 0001454881 scopus 로고
    • Canonical reduction of mechanical systems invariant under abelian group actions with an application to celestial mechanics
    • W. J. Satzer: Canonical reduction of mechanical systems invariant under abelian group actions with an application to celestial mechanics, Indiana Univ. Math. J. 26 (1977), 951-976.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 951-976
    • Satzer, W.J.1
  • 32
    • 0042805662 scopus 로고
    • Smooth functions invariant under the action of a compact Lie group
    • G. W. Schwarz: Smooth functions invariant under the action of a compact Lie group, Topology 14 (1974), 63-68.
    • (1974) Topology , vol.14 , pp. 63-68
    • Schwarz, G.W.1
  • 33
    • 0040381637 scopus 로고
    • Abstract covariant derivative
    • R. Sikorski: Abstract covariant derivative, Colloquium Math. 18 (1967), 251-272.
    • (1967) Colloquium Math. , vol.18 , pp. 251-272
    • Sikorski, R.1
  • 34
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • R. Sjamaar and E. Lerman: Stratified symplectic spaces and reduction, Ann. Math. 134 (1991), 375-422.
    • (1991) Ann. Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2
  • 36
    • 0003246009 scopus 로고
    • Lectures on the Geometry of Poisson Manifolds
    • Birkhäuser
    • I. Vaisman: Lectures on the Geometry of Poisson Manifolds, Progress in Mathematics, 118, Birkhäuser, 1994.
    • (1994) Progress in Mathematics , vol.118
    • Vaisman, I.1
  • 37
    • 0032039820 scopus 로고    scopus 로고
    • Implicit Hamiltonian systems with symmetry
    • A. J. van der Schaft: Implicit Hamiltonian systems with symmetry, Rep. Math. Phys. 41 (1998), 203-221.
    • (1998) Rep. Math. Phys. , vol.41 , pp. 203-221
    • van der Schaft, A.J.1
  • 39
    • 0000278487 scopus 로고
    • On the Hamiltonian formulation of nonholonomic mechanical systems
    • A. J. van der Schaft and B. M. Maschke: On the Hamiltonian formulation of nonholonomic mechanical systems, Rep. Math. Phys. 34 (1994), 225-232.
    • (1994) Rep. Math. Phys. , vol.34 , pp. 225-232
    • van der Schaft, A.J.1    Maschke, B.M.2
  • 40
  • 41
    • 0347523632 scopus 로고
    • Mathematical modeling of constrained Hamiltonian systems
    • Preprints of the 3rd Nonlinear Control Systems Design Symposium, NOLCOS, Tahoe City, CA
    • A. J. van der Schaft and B. M. Maschke: Mathematical modeling of constrained Hamiltonian systems. In Preprints of the 3rd Nonlinear Control Systems Design Symposium, NOLCOS, Tahoe City, CA, 1995.
    • (1995)
    • van der Schaft, A.J.1    Maschke, B.M.2
  • 42
    • 0003207640 scopus 로고    scopus 로고
    • Interconnected mechanical systems, part I: Geometry of interconnection and implicit Hamiltonian systems
    • A. Astolfi, D. J. N Limebeer, C. Melchiorri, A. Tornambè, and R. B. Vinter (eds.), Imperial College Press
    • A. J. van der Schaft and B. M. Maschke: Interconnected mechanical systems, part I: geometry of interconnection and implicit Hamiltonian systems. In A. Astolfi, D. J. N Limebeer, C. Melchiorri, A. Tornambè, and R. B. Vinter (eds.), Modelling and Control of Mechanical Systems, pp. 1-15. Imperial College Press, 1997.
    • (1997) Modelling and Control of Mechanical Systems , pp. 1-15
    • van der Schaft, A.J.1    Maschke, B.M.2
  • 43
    • 0004109271 scopus 로고
    • 2nd ed., Princeton University Press, Princeton
    • H. Weyl: The Classical Groups, 2nd ed., Princeton University Press, Princeton 1946.
    • (1946) The Classical Groups
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.