4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard
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Gérard Grangier (1984)
Publications du Département de mathématiques (Lyon)
Ignacio Aparicio, Luis Floría (1997)
Extracta Mathematicae
The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.
M. De León, E. Merino, J. A. Oubiña, M. Salgado (1994)
Annales de l'I.H.P. Physique théorique
Renate Schaaf (1985)
Journal für die reine und angewandte Mathematik
Agnès Tourin (1992)
Numerische Mathematik
Adriano Montanaro (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...
Knill, Oliver (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Fedorov, Yuri N. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Boyd, J.N., Raychowdhury, P.N. (1991)
International Journal of Mathematics and Mathematical Sciences
Luis Floría (1994)
Extracta Mathematicae
Damianou, Pantelis A., Magri, Franco (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Monika Havelková (2011)
Communications in Mathematics
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.
Delshams, Amadeu, de la Llave, Rafael, Seara, Tere M. (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Albu, I. D., Opriş, D. (1999)
Novi Sad Journal of Mathematics
Cherkis, Sergey A. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Jorba, Àngel (1999)
Experimental Mathematics
M. de León, J. C. Marrero, D. Martín de Diego (2003)
Banach Center Publications
A new geometrical setting for classical field theories is introduced. This description is strongly inspired by the one due to Skinner and Rusk for singular lagrangian systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.
Enrico Massa, Stefano Vignolo (2003)
Extracta Mathematicae
François Gay-Balmaz, Tudor S. Ratiu (2010)
Annales de l’institut Fourier
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
Enrico Massa, Enrico Pagani (1997)
Annales de l'I.H.P. Physique théorique
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