메뉴 건너뛰기




Volumn 13, Issue 2, 1998, Pages 123-165

The energy-momentum method for the stability of non-holonomic systems

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ENERGY CONSERVATION; THEOREM PROVING;

EID: 0032099856     PISSN: 02681110     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119808806257     Document Type: Article
Times cited : (63)

References (81)
  • 2
    • 26644467107 scopus 로고
    • Sur l'intégration des équations du mouvement d'un corps pesant de révolution roulant par une arête circulaire sur un plan horizontal; cas parficulier du cerceau
    • Appel, P. (1900) Sur l'intégration des équations du mouvement d'un corps pesant de révolution roulant par une arête circulaire sur un plan horizontal; cas parficulier du cerceau. Rendiconti del circolo matematico di Palermo 14, 1-6.
    • (1900) Rendiconti del Circolo Matematico di Palermo , vol.14 , pp. 1-6
    • Appel, P.1
  • 3
    • 0001356905 scopus 로고
    • Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits
    • Arnold, V. I. (1966) Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits. Annales Institut Fourier, Grenoble 16, 319-361.
    • (1966) Annales Institut Fourier, Grenoble , vol.16 , pp. 319-361
    • Arnold, V.I.1
  • 7
    • 0002347915 scopus 로고
    • On the dynamics and control of nonholonomic systems on Riemannian manifolds
    • Bordeaux
    • Bloch, A. M. and Crouch, P. (1992) On the dynamics and control of nonholonomic systems on Riemannian manifolds. Proceedings of NOLCOS '92, Bordeaux, pp. 368-372.
    • (1992) Proceedings of NOLCOS '92 , pp. 368-372
    • Bloch, A.M.1    Crouch, P.2
  • 8
    • 0002175497 scopus 로고
    • Nonholonomic control systems on Riemannian manifolds
    • Bloch, A. M. and Crouch, P. (1995) Nonholonomic control systems on Riemannian manifolds. SIAM Journal on Control 37, 126-148.
    • (1995) SIAM Journal on Control , vol.37 , pp. 126-148
    • Bloch, A.M.1    Crouch, P.2
  • 14
    • 0013045880 scopus 로고
    • The rigid body dynamics of unidirectional spin
    • Bondi, H. (1986) The rigid body dynamics of unidirectional spin. Proceeding of the Royal Society London 405, 265-274.
    • (1986) Proceeding of the Royal Society London , vol.405 , pp. 265-274
    • Bondi, H.1
  • 15
    • 0002433662 scopus 로고
    • Nonholonomic kinematics and the role of elliptic functions in constructive controllability
    • eds Z. Li and J. F. Canny; Kluwer, Dordrecht
    • Brockett, R. W. and Dai, L. (1992) Nonholonomic kinematics and the role of elliptic functions in constructive controllability. Nonholonomic Motion Planning (eds Z. Li and J. F. Canny; Kluwer, Dordrecht), pp. 1-22.
    • (1992) Nonholonomic Motion Planning , pp. 1-22
    • Brockett, R.W.1    Dai, L.2
  • 19
    • 0040456306 scopus 로고
    • On some feasible generalization of the theorem of area, with an application to the problem of rolling spheres
    • Reproduced in Chaplygin (1954), pp. 434-454
    • Chaplygin, S. A. (1897b) On some feasible generalization of the theorem of area, with an application to the problem of rolling spheres (in Russian). Matematicheskiǐ sbornik XX, 1-32. (Reproduced in Chaplygin (1954), pp. 434-454.)
    • (1897) Matematicheskiǐ Sbornik , vol.20 , pp. 1-32
    • Chaplygin, S.A.1
  • 20
    • 0010789997 scopus 로고
    • On a rolling sphere on a horizontal plane
    • Reproduced in Chaplygin (1949), pp. 72-99 and Chaplygin (1954), pp. 455-471
    • Chaplygin, S. A. (1903) On a rolling sphere on a horizontal plane (in Russian). Matematicheskiǐ sbornik XXIV, 139-168. (Reproduced in Chaplygin (1949), pp. 72-99 and Chaplygin (1954), pp. 455-471.)
    • (1903) Matematicheskiǐ Sbornik , vol.24 , pp. 139-168
    • Chaplygin, S.A.1
  • 21
    • 0037823663 scopus 로고
    • On the theory of the motion of nonholonomic systems. Theorem on the reducing factor
    • Reproduced in Chaplygin (1949), pp. 28-38 and Chaplygin (1954), pp. 426-433
    • Chaplygin, S. A. (1911) On the theory of the motion of nonholonomic systems. Theorem on the reducing factor (in Russian). Matematicheskiǐ sbornik XXVIII, 303-314. (Reproduced in Chaplygin (1949), pp. 28-38 and Chaplygin (1954), pp. 426-433.)
    • (1911) Matematicheskiǐ Sbornik , vol.28 , pp. 303-314
    • Chaplygin, S.A.1
  • 24
    • 84963254961 scopus 로고
    • A note on symmetry and stability for fluid flows
    • Chern, S. J. and Marsden, J. E. (1990) A note on symmetry and stability for fluid flows. Geo. Astro. Fluid Dynamics 51, 1-4.
    • (1990) Geo. Astro. Fluid Dynamics , vol.51 , pp. 1-4
    • Chern, S.J.1    Marsden, J.E.2
  • 28
    • 0346069298 scopus 로고    scopus 로고
    • Birkhauser, Basel
    • Cushman, R., Hermans, J. and Kemppainen, D. (1996) The rolling disc. Nonlinear Dynamical Systems and Chaos (Groningen, 1995), pp. 21-60, Progr. Nonlinear Differential Equations Appl. 19 (Birkhauser, Basel).
    • Progr. Nonlinear Differential Equations Appl. , vol.19
  • 31
    • 0001796616 scopus 로고
    • Die Lagrange-Eulerschen Gleichungen der Mechanik
    • Hamel, G. (1904) Die Lagrange-Eulerschen Gleichungen der Mechanik. Zeitschrift für Mathematik und Physik 50, 1-57.
    • (1904) Zeitschrift für Mathematik und Physik , vol.50 , pp. 1-57
    • Hamel, G.1
  • 33
    • 0039271723 scopus 로고
    • A symmetric sphere rolling on a surface
    • Hermans, J. (1995b) A symmetric sphere rolling on a surface. Nonlinearity 8, 493-515.
    • (1995) Nonlinearity , vol.8 , pp. 493-515
    • Hermans, J.1
  • 34
    • 21344497588 scopus 로고
    • The geometry of the plate-ball problem
    • Jurdjevic, V. (1993) The geometry of the plate-ball problem. Arch. Rat. Mech. An 124, 305-328.
    • (1993) Arch. Rat. Mech. An , vol.124 , pp. 305-328
    • Jurdjevic, V.1
  • 35
    • 0141586648 scopus 로고
    • On the problem of steady motions of nonholonomic systems
    • Karapetyan, A. V. (1980) On the problem of steady motions of nonholonomic systems. Applied Mathematics and Mechanics 44, 418-426.
    • (1980) Applied Mathematics and Mechanics , vol.44 , pp. 418-426
    • Karapetyan, A.V.1
  • 36
    • 0019753996 scopus 로고
    • On stability of steady state motions of a heavy solid body on an absolutely rough horizontal plane
    • Karapetyan, A. V. (1981) On stability of steady state motions of a heavy solid body on an absolutely rough horizontal plane. Applied Mathematics and Mechanics 45, 604-608.
    • (1981) Applied Mathematics and Mechanics , vol.45 , pp. 604-608
    • Karapetyan, A.V.1
  • 37
    • 0020880397 scopus 로고
    • Stability of steady motions of systems of a certain type
    • Karapetyan, A. V. (1983) Stability of steady motions of systems of a certain type. Mechanics of Solids 18, 41-47.
    • (1983) Mechanics of Solids , vol.18 , pp. 41-47
    • Karapetyan, A.V.1
  • 38
    • 84995037667 scopus 로고
    • Geometric phases and robotic locomotion
    • Also available as Caltech technical report CIT/CDS 94-014
    • Kelly, S. D. and Murray, R. M. (1995) Geometric phases and robotic locomotion. Journal of Robotic Systems. Also available as Caltech technical report CIT/CDS 94-014.
    • (1995) Journal of Robotic Systems
    • Kelly, S.D.1    Murray, R.M.2
  • 39
    • 0000768876 scopus 로고
    • Reduction of some classical nonholonomic systems with symmetry
    • Koiller, J. (1992) Reduction of some classical nonholonomic systems with symmetry. Arch. Rat. Mech. An. 118, 113-148.
    • (1992) Arch. Rat. Mech. An. , vol.118 , pp. 113-148
    • Koiller, J.1
  • 40
    • 0031145153 scopus 로고    scopus 로고
    • Optimal control for holonomic and nonholonomic mechanical systems with symmetry and Lagrangian reduction
    • Koon, W. S. and Marsden, J. E. (1997a) Optimal control for holonomic and nonholonomic mechanical systems with symmetry and Lagrangian reduction. SIAM Journal of Control and Optimization 35, 901-929.
    • (1997) SIAM Journal of Control and Optimization , vol.35 , pp. 901-929
    • Koon, W.S.1    Marsden, J.E.2
  • 41
    • 0031206274 scopus 로고    scopus 로고
    • The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems
    • Koon, W. S. and Marsden, J. E. (1997b) The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems. Reports on Mathematical Physics 40, 21-62.
    • (1997) Reports on Mathematical Physics , vol.40 , pp. 21-62
    • Koon, W.S.1    Marsden, J.E.2
  • 43
    • 0000520262 scopus 로고
    • Ueber eine ziemlich verbreitete unrichtige Behandlungsweise eines Problemes der rollenden Bewegung und insbesondere über kleine rollende Schwingungen um eine Gleichgewichtslage
    • Korteweg, D. (1899) Ueber eine ziemlich verbreitete unrichtige Behandlungsweise eines Problemes der rollenden Bewegung und insbesondere über kleine rollende Schwingungen um eine Gleichgewichtslage. Nieuw Archiefvoor Wiskunde 4, 130-155.
    • (1899) Nieuw Archiefvoor Wiskunde , vol.4 , pp. 130-155
    • Korteweg, D.1
  • 45
    • 0040456322 scopus 로고
    • Eulerian many-body problems
    • Krishnaprasad, P. S. (1989) Eulerian many-body problems. Cont. Math. AMS 97, 187-208.
    • (1989) Cont. Math. AMS , vol.97 , pp. 187-208
    • Krishnaprasad, P.S.1
  • 48
    • 0003154764 scopus 로고
    • On the stability of motion in a sense of Lyapunov
    • Malkin, I. G. (1938) On the stability of motion in a sense of Lyapunov (in Russian). Matematicheskiǐ sbornik XXXV, 47-101.
    • (1938) Matematicheskiǐ Sbornik , vol.35 , pp. 47-101
    • Malkin, I.G.1
  • 49
    • 0020926049 scopus 로고
    • On dynamics of a solid on an absolutely rough plane
    • Markeev, A. P. (1983) On dynamics of a solid on an absolutely rough plane. Applied Mathematics and Mechanics 47, 473-478.
    • (1983) Applied Mathematics and Mechanics , vol.47 , pp. 473-478
    • Markeev, A.P.1
  • 52
    • 0002893048 scopus 로고
    • Lagrangian reduction and the double spherical pendulum
    • Marsden, J. E. and Scheurle, J. (1993a) Lagrangian reduction and the double spherical pendulum. ZAMP 44, 17-43.
    • (1993) ZAMP , vol.44 , pp. 17-43
    • Marsden, J.E.1    Scheurle, J.2
  • 54
    • 0003643366 scopus 로고
    • An Introduction to Mechanics and Symmetry
    • Springer-Verlag, New York
    • Marsden, J. E. and Ratiu, T. S. (1994) An Introduction to Mechanics and Symmetry, Texts in Appl. Math. 17 (Springer-Verlag, New York).
    • (1994) Texts in Appl. Math. , vol.17
    • Marsden, J.E.1    Ratiu, T.S.2
  • 57
    • 0004190360 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • Milnor, J. (1963) Morse Theory (Princeton University Press, Princeton, New Jersey).
    • (1963) Morse Theory
    • Milnor, J.1
  • 58
    • 49949135124 scopus 로고
    • On stability of stationary motions of holonomic and nonholonomic systems
    • Neimark, Ju. I. and Fufaev, N. A. (1966) On stability of stationary motions of holonomic and nonholonomic systems. Journal of Applied Mathematics (PMM) 30, 293-300.
    • (1966) Journal of Applied Mathematics (PMM) , vol.30 , pp. 293-300
    • Neimark, Ju.I.1    Fufaev, N.A.2
  • 60
    • 0030190139 scopus 로고    scopus 로고
    • The dynamics of rolling disks and sliding disks
    • O'Reilly, O. M. (1996) The dynamics of rolling disks and sliding disks. Nonlinear Dynamics 10, 287-305.
    • (1996) Nonlinear Dynamics , vol.10 , pp. 287-305
    • O'Reilly, O.M.1
  • 63
    • 0020912220 scopus 로고
    • Asymptotic solution of the equations of motion for a celtic stone
    • Pascal, M. (1983) Asymptotic solution of the equations of motion for a celtic stone. Applied Mathematics and Mechanics 47, 269-276.
    • (1983) Applied Mathematics and Mechanics , vol.47 , pp. 269-276
    • Pascal, M.1
  • 64
    • 0022941074 scopus 로고
    • The use of the method of averaging to study nonlinear oscillations of the celtic stone
    • Pascal, M. (1986) The use of the method of averaging to study nonlinear oscillations of the celtic stone. Applied Mathematics and Mechanics 50, 520-522.
    • (1986) Applied Mathematics and Mechanics , vol.50 , pp. 520-522
    • Pascal, M.1
  • 65
    • 0001229661 scopus 로고
    • Sur une forme nouvelle des equations de la mecanique
    • Poincaré, H. (1901) Sur une forme nouvelle des equations de la mecanique. CR Acad. Sci. 132, 369-371.
    • (1901) CR Acad. Sci. , vol.132 , pp. 369-371
    • Poincaré, H.1
  • 68
    • 0002985376 scopus 로고
    • Stability of relative equilibria I: The reduced energy-momentum method
    • Simo, J. C., Lewis, D. R. and Marsden, J. E. (1991) Stability of relative equilibria I: the reduced energy-momentum method. Arch. Rat. Mech. An. 115, 15-59.
    • (1991) Arch. Rat. Mech. An. , vol.115 , pp. 15-59
    • Simo, J.C.1    Lewis, D.R.2    Marsden, J.E.3
  • 69
    • 22244441450 scopus 로고    scopus 로고
    • Topology and mechanics
    • Smale, S. (1970) Topology and mechanics. Inv. Math. 10, 305-331; 11, 45-64.
    • (1970) Inv. Math. , vol.10 , pp. 305-331
    • Smale, S.1
  • 70
    • 22244441450 scopus 로고    scopus 로고
    • Smale, S. (1970) Topology and mechanics. Inv. Math. 10, 305-331; 11, 45-64.
    • Inv. Math. , vol.11 , pp. 45-64
  • 71
    • 0039271731 scopus 로고
    • Developments of some of Lagrange's ideas in the works of Russian and Soviet mechanicians
    • Atti della Accademia delle Scienze di Torino
    • Sumbatov, A. S. (1992) Developments of some of Lagrange's ideas in the works of Russian and Soviet mechanicians. La Mécanique Analytique de Lagrange ei Son héritage (Atti della Accademia delle Scienze di Torino), Supp. 2, Vol. 126, pp. 169-200.
    • (1992) La Mécanique Analytique de Lagrange ei Son Héritage , vol.126 , Issue.2 SUPPL. , pp. 169-200
    • Sumbatov, A.S.1
  • 74
    • 0000237735 scopus 로고
    • Lagrangian mechanics in invariant form
    • Vershik, A. M. and Faddeev, L. D. (1981) Lagrangian mechanics in invariant form. Sel. Math. Sov. 1, 339-350.
    • (1981) Sel. Math. Sov. , vol.1 , pp. 339-350
    • Vershik, A.M.1    Faddeev, L.D.2
  • 75
    • 0003041322 scopus 로고
    • Nonholonomic dynamical systems, geometry of distributions and variational problems
    • (eds V. Arnold and S. P. Novikov; Springer-Verlag, New York)
    • Vershik, A. M. and Gershkovich, V. Ya. (1994) Nonholonomic dynamical systems, geometry of distributions and variational problems. Dynamical Systems VII (eds V. Arnold and S. P. Novikov; Springer-Verlag, New York), pp. 1-81.
    • (1994) Dynamical Systems VII , pp. 1-81
    • Vershik, A.M.1    Gershkovich, V.Ya.2
  • 81
    • 0001084718 scopus 로고
    • The geometry of the Routh problem
    • Zenkov, D. V. (1995) The geometry of the Routh problem. Journal of Nonlinear Science 5, 503-519.
    • (1995) Journal of Nonlinear Science , vol.5 , pp. 503-519
    • Zenkov, D.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.