Accès à distance ? S'identifier sur le proxy UCLouvain
A Simple Variational Approach To a Converse of the Lagrange-dirichlet Theorem
Primary tabs
Document type | Article de périodique (Journal article) – Article de recherche |
---|---|
Access type | Accès restreint |
Publication date | 1992 |
Language | Anglais |
Journal information | "Archive for Rational Mechanics and Analysis" - Vol. 120, no. 4, p. 327-335 (1992) |
Peer reviewed | yes |
Publisher | Springer Verlag (New York) |
issn | 0003-9527 |
e-issn | 1432-0673 |
Publication status | Publié |
Affiliation | UCL - SC/MATH - Département de mathématique |
Links |
- M. A. Balitinov, On instability of the position of equilibrium of a Hamiltonian system, Prikl. Mat. Mekh. (J. Appl. Math. Mech.) 42 (1978), 582?587.
- S. V. Bolotin & V. V. Kozlov, on the asymptotic solutions of the equations of dynamics, Moscow Univ. Math. Bull. 35 (1980), 82?88.
- S. D. Furta, On asymptotic solutions of the equations of motion of mechanical sytems, Prikl. Mat. Mekh. 50 (1986), 726?730.
- P. Hagedorn, Die Umkehrung der Stabilit�tss�tze von Lagrange-Dirichlet und Routh, Arch. Rational Mech. Anal. 42 (1971), 281?316.
- P. Hagedorn, Eine zus�tzliche Bemerkung zu meiner Arbeit: Die Umkehrung der Stabilit�tss�tze von Lagrange-Dirichlet und Routh, Arch. Rational Mech. Anal. 47 (1972), 395.
- A. V. Karapetjan, On the inversion of the Routh theorem, Vestnik Moskov Univ. Ser. 1 Mat. Meh. 28 (1973), 65?69.
- V. V. Kozlov, Instability of equilibrium in a potential field, Russian Math. Surveys 36 (1981), 238?239.
- V. V. Kozlov, On the instability of equilibrium in a potential field, Russian Math. Surveys 36 (1981), 256?257.
- V. V. Kozlov, Asymptotic solutions of equations of classical mechanics, Prikl. Mat. Mekh. (J. Appl. Math. Mech.) 46 (1982), 454?457.
- V. V. Kozlov, Calculus of variations in the large and classical mechanics, Russian Mathematics Survey 40 (1985), 37?71.
- V. V. Kozlov, Asymptotic motions and the inversion of the Lagrange-Dirichlet Theorem, Prikl. Mat. Mekh. (J. Appl. Math. Mech.) 50 (1987), 719?725.
- V. V. Kozlov & V. V. Palamodov, On asymptotic solutions of the equations of classical mechanics, Soviet Math. Dokl. 25 (1982), 335?339.
- J. L. Lagrange, M�canique analytique, Paris, 1788.
- M. Laloy, On the inversion of Lagrange-Dirichlet Theorem in the case of an analytical potential, Report 107 SMAM, Univ. Catholique de Louvain, 1977.
- M. Laloy & P. Habets, On the instability of a two-dimensional conservative mechanical system with analytical potential, in Equadiff 78, Firenze, 1978, 149?164.
- M. Laloy & K. Peiffer, On the instability of equilibrium when the potential has a non-strict local minimum, Arch. Rational Mech. Anal. 78 (1982), 213?222.
- Lejeune Dirichlet G., Über die Stabilität des Gleichgewichts., 10.1515/crll.1846.32.85
- Liubushin E.A., On instability of equilibrium when the force function is not a maximum, 10.1016/0021-8928(80)90140-9
- Mawhin Jean, Willem Michel, Critical Point Theory and Hamiltonian Systems, ISBN:9781441930897, 10.1007/978-1-4757-2061-7
- C. Maffei, V. Moauro & P. Negrini, On the inversion of the Lagrange-Dirichlet Theorem in a case of nonhomogeneous potential, Diff. Integral Eqs. 4 (1991), 767?782.
- V. Moauro & P. Negrini, On the inversion of the Lagrange-Dirichlet Theorem, Diff. Integral Eqs. 2 (1989), 471?478.
- P. Painlev�, Sur la stabilit� de l'�quilibre, C.R. Acad. Sci. Paris 138 (1904), 1170?1174.
- V. V. Palamodov, Stability of equilibrium in a potential field, Functional Anal. Appl. 11 (1978), 227?289.
- K. Peiffer, An example of non isolated equilibrium with maximum potential, stabilized by dissipative forces, Z. angew. Math. Phys. 30 (1979), 835?837.
- K. Peiffer, On the inversion of Lagrange-Dirichlet Theorem, RSM UCL 162, 1989, to appear in Prikl. Mat. Mekh. (shorter version in The Lyapunov Functions, Method and Applications, Borne & Matrosov eds., Baltzer AG, 1990, 9?13).
- K. Peiffer & P. Carlier, A remark on the inversion of Lagrange-Dirichlet's theorem, Qualitative theory of Differential Equations, Szeged, 1988; Coll. Math. Soc. J. Bolyai 53, Noordhoff, 1990, 473?484.
- Rouche N., Habets P., Laloy M., Stability Theory by Liapunov’s Direct Method, ISBN:9780387902586, 10.1007/978-1-4684-9362-7
- V. V. Rumiantsev, On stability of motions of conservative systems, in Qualitative Theory of Differential Equations, Szeged, 1979, Coll. Math. Soc. J. Bolyai, 30 vol. II, North Holland, Amsterdam, 1981, 865?901.
- M. Sofer, On the inversion of the Lagrange-Dirichlet stability Theorem ? mechanical and generalized systems, Z. angew. Math. Phys. 34 (1983), 1?12.
- S. D. Taliaferro, An inversion of the Lagrange-Dirichlet stability Theorem, Arch. Rational Mech. Anal. 73 (1980), 183?190.
- S. D. Taliaferro, Stability for two-dimensional analytic potentials, J. Diff. Eqs. 35 (1980), 248?265.
- S. D. Taliaferro, Instability of an equilibrium in a potential field, Arch. Rational Mech. Anal. (1990), 183?194.
- E. W. C. Van Groesen, Analytical mini-max methods for Hamiltonian brake orbits of prescribed energy, J. Math. Anal. Appl. 132 (1988), 1?12.
- E. W. C. Van Groesen, Hamiltonian flow on an energy integral: 240 years after the Euler-Maupertuis principle, Proc. Sixth Scheveningen Conference, 1984.
- V. A. Vladimirov & V. V. Rumiantsev, On the inversion of Lagrange's Theorem for a rigid body with a cavity containing an ideal liquid, Prikl. Mat. Mekh. (J. Appl. Math. Mech.) 53 (1989), 608?612.
- Vladimirov V.A., Rumyantsev V.V., Inversion of lagrange's theorem for a rigid body with a cavity containing a viscous liquid, 10.1016/0021-8928(90)90027-8
- A. Winter, The Analytical Foundations of Celestial Mechanics, Princeton Univ. Press, Princeton, 1941.
Bibliographic reference | Hagedorn, P. ; Mawhin, Jean. A Simple Variational Approach To a Converse of the Lagrange-dirichlet Theorem. In: Archive for Rational Mechanics and Analysis, Vol. 120, no. 4, p. 327-335 (1992) |
---|---|
Permanent URL | http://hdl.handle.net/2078.1/50128 |