메뉴 건너뛰기




Volumn 52, Issue 1, 2004, Pages 1-27

Dynamics on Leibniz manifolds

Author keywords

Hamiltonian mechanics; Leibniz manifolds; Non holonomic mechanics; Poisson geometry

Indexed keywords


EID: 3242893069     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2004.01.002     Document Type: Article
Times cited : (56)

References (34)
  • 3
    • 0003149163 scopus 로고    scopus 로고
    • Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction
    • Alber M.S. Luther G.G. Marsden J.E. Robbins J.M. Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction Physica D 123 1998 271-290
    • (1998) Physica D , vol.123 , pp. 271-290
    • Alber, M.S.1    Luther, G.G.2    Marsden, J.E.3    Robbins, J.M.4
  • 4
    • 0002881562 scopus 로고
    • A universal reduction procedure for Hamiltonian group actions
    • T.S. Ratiu (Ed.), Springer-Verlag
    • Arms J.M. Cushman R. Gotay M.J. A universal reduction procedure for Hamiltonian group actions, in: T.S. Ratiu (Ed.), The Geometry of Hamiltonian Systems, Springer-Verlag, 1991, pp. 33-51.
    • (1991) The Geometry of Hamiltonian Systems , pp. 33-51
    • Arms, J.M.1    Cushman, R.2    Gotay, M.J.3
  • 7
    • 0347945203 scopus 로고    scopus 로고
    • Asymptotic Hamiltonian dynamics: The Toda lattice, the three-wave interaction and the nonholonomic Chaplygin sleigh
    • Bloch A.M. Asymptotic Hamiltonian dynamics: the Toda lattice, the three-wave interaction and the nonholonomic Chaplygin sleigh Physica D 141 2000 297-315
    • (2000) Physica D , vol.141 , pp. 297-315
    • Bloch, A.M.1
  • 8
    • 0346241309 scopus 로고    scopus 로고
    • Interdisciplinary Applied Mathematics, Springer-Verlag
    • Bloch A. Nonholonomic Mechanics and Control, vol. 24, Interdisciplinary Applied Mathematics, Springer-Verlag, 2003.
    • (2003) Nonholonomic Mechanics and Control , vol.24
    • Bloch, A.1
  • 11
    • 0001782325 scopus 로고
    • A theory of nonlinear networks. Part I and Part II
    • 1-33 and
    • Brayton R.K. Moser J.K. A theory of nonlinear networks. Part I and Part II, Quart. Appl. Math. 22 (1964) 1-33 and 81-104.
    • (1964) Quart. Appl. Math. , vol.22 , pp. 81-104
    • Brayton, R.K.1    Moser, J.K.2
  • 12
    • 0024175873 scopus 로고
    • Dynamical systems that sort lists and solve linear programming systems
    • Brockett R.W. Dynamical systems that sort lists and solve linear programming systems Proc. IEEE 27 1988 799-803
    • (1988) Proc. IEEE , vol.27 , pp. 799-803
    • Brockett, R.W.1
  • 13
    • 0002412868 scopus 로고
    • Dynamical systems that sort lists and solve linear programming systems
    • Brockett R.W. Dynamical systems that sort lists and solve linear programming systems Linear Algebra Appl. 146 1991 79-91
    • (1991) Linear Algebra Appl. , vol.146 , pp. 79-91
    • Brockett, R.W.1
  • 14
    • 0010189217 scopus 로고
    • Differential geometry and the design of gradient algorithms
    • Brockett R.W. Differential geometry and the design of gradient algorithms Proc. Symp. Pure Math. AMS 54I 1993 69-92
    • (1993) Proc. Symp. Pure Math. AMS , vol.54 I , pp. 69-92
    • Brockett, R.W.1
  • 15
    • 0033130297 scopus 로고    scopus 로고
    • On almost-Poisson structures in nonholonomic mechanics
    • Cantrijn F. de León M. Martín de Diego D. On almost-Poisson structures in nonholonomic mechanics Nonlinearity 123 1999 721-737
    • (1999) Nonlinearity , vol.12 , Issue.3 , pp. 721-737
    • Cantrijn, F.1    de León, M.2    Martín de Diego, D.3
  • 17
    • 0019612867 scopus 로고
    • Geometric structures in systems theory
    • Crouch P.E. Geometric structures in systems theory Proc. IEE D: Contr. Theory Appl. 1285 1981 242-252
    • (1981) Proc. IEE D: Contr. Theory Appl. , vol.128 , Issue.5 , pp. 242-252
    • Crouch, P.E.1
  • 19
    • 0033196431 scopus 로고    scopus 로고
    • Algebroids-general differential calculus on vector bundles
    • Grabowski J. Urbanski P. Algebroids-general differential calculus on vector bundles J. Geom. Phys. 31 1999 111-141
    • (1999) J. Geom. Phys. , vol.31 , pp. 111-141
    • Grabowski, J.1    Urbanski, P.2
  • 21
    • 0002390971 scopus 로고
    • Une version non-commutative des algèbres de Lie: Les algèbres de Leibniz
    • Loday J.-L. Une version non-commutative des algèbres de Lie: Les algèbres de Leibniz L'Enseignement Mathématique 39 1993 269-293
    • (1993) L'Enseignement Mathématique , vol.39 , pp. 269-293
    • Loday, J.-L.1
  • 22
    • 0000194890 scopus 로고
    • Reduction of constrained mechanical systems and stability of relative equilibria
    • Marle C.-M. Reduction of constrained mechanical systems and stability of relative equilibria Comm. Math. Phys. 174 1995 295-318
    • (1995) Comm. Math. Phys. , vol.174 , pp. 295-318
    • Marle, C.-M.1
  • 23
    • 0032132873 scopus 로고    scopus 로고
    • Various approaches to conservative and nonconservative nonholonomic systems
    • Marle C.-M. Various approaches to conservative and nonconservative nonholonomic systems Rep. Math. Phys. 42 1998 211-229
    • (1998) Rep. Math. Phys. , vol.42 , pp. 211-229
    • Marle, C.-M.1
  • 24
    • 0003610563 scopus 로고
    • London Mathematical Society Lecture Note Series, 2nd ed., Cambridge University Press, Cambridge
    • Marsden J.E. Lectures on Mechanics, London Mathematical Society Lecture Note Series, vol. 174, 2nd ed., Cambridge University Press, Cambridge, 1992.
    • (1992) Lectures on Mechanics , vol.174
    • Marsden, J.E.1
  • 26
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • Marsden J.E. Weinstein A. Reduction of symplectic manifolds with symmetry Rep. Math. Phys. 51 1974 121-130
    • (1974) Rep. Math. Phys. , vol.5 , Issue.1 , pp. 121-130
    • Marsden, J.E.1    Weinstein, A.2
  • 27
    • 0001379563 scopus 로고
    • A paradigm for joined Hamiltonian and dissipative systems
    • Morrison P.J. A paradigm for joined Hamiltonian and dissipative systems Physica D 18 1986 410-419
    • (1986) Physica D , vol.18 , pp. 410-419
    • Morrison, P.J.1
  • 28
    • 0002083047 scopus 로고    scopus 로고
    • Singular reduction of Poisson manifolds
    • Ortega J.-P. Ratiu T.S. 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
  • 29
    • 8644228948 scopus 로고    scopus 로고
    • Momentum Maps and Hamiltonian Reduction
    • Birkhäuser Verlag
    • Ortega J.-P. Ratiu T.S. Momentum Maps and Hamiltonian Reduction, Progress in Mathematics, vol. 222, Birkhäuser Verlag, 2003.
    • (2003) Progress in Mathematics , vol.222
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 30
    • 54649083037 scopus 로고    scopus 로고
    • The Volterra lattice as a gradient flow
    • Penskoï A.V. The Volterra lattice as a gradient flow Regul. Khaoticheskaya Din. 31 1998 76-77
    • (1998) Regul. Khaoticheskaya Din. , vol.3 , Issue.1 , pp. 76-77
    • Penskoï, A.V.1
  • 31
    • 3242882515 scopus 로고    scopus 로고
    • Reduction and stability of dynamical systems on Poisson and Leibniz manifolds
    • Ph.D. Thesis, Institut Non Linéaire de Nice, Université de Nice Sophia-Antipolis, in preparation
    • Planas-Bielsa V. Reduction and stability of dynamical systems on Poisson and Leibniz manifolds, Ph.D. Thesis, Institut Non Linéaire de Nice, Université de Nice Sophia-Antipolis, in preparation.
    • Planas-Bielsa, V.1
  • 32
    • 0345573695 scopus 로고    scopus 로고
    • Almost Poisson spaces and nonholonomic singular reduction
    • Sniatycki J. Almost Poisson spaces and nonholonomic singular reduction Rep. Math. Phys. 48 2001 235-248
    • (2001) Rep. Math. Phys. , vol.48 , pp. 235-248
    • Sniatycki, J.1
  • 34
    • 0000278487 scopus 로고
    • On the Hamiltonian formulation of nonholonomic mechanical systems
    • van der Schaft A.J. Maschke B.M. On the Hamiltonian formulation of nonholonomic mechanical systems Rep. Math. Phys. 34 1994 225-233
    • (1994) Rep. Math. Phys. , vol.34 , pp. 225-233
    • van der Schaft, A.J.1    Maschke, B.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.