SIMON-PETIT, Alicia (2015) Gravitational Dynamical Systems PFE - Project Graduation, ENSTA.

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In order to investigate dynamics at small cosmological scales, the dynamics of stars or massive particles in a central potential is studied. The isochrone model, first introduced by Michel Hénonin 1959, is a special case well describing the structure of numerous observed globular clusters and setting a specific link between the Coulomb and Kepler potentials which properties have been derived to highlight their duality. The reminding of Liouville integrability and generalised Gorringe-Leach equations eventually enable the further investigation of the isochrone potential.The general theory of relativity established by Einstein is on the other hand used to un- derstand the cosmological reasons that have led him to introduce a new universal constant, the cosmological constant, to describe a static universe in its whole. This is studied before examining the cosmological principle and Friedmann-Lemaˆıtre-Robertson-Walker equations that describe the fundamental properties of the universe at large scales today. The notion of observable and key elements, necessary to the numerical simulation I have made of this model and its validation,are also explained.

Item Type:Thesis (PFE - Project Graduation)
Uncontrolled Keywords:Isochrone cluster, central potential, harmonic potential, Hooke potential, gra- vitationnal potential, Kepler potential, symetry, conserved quantities, Jauch-Hill-Fradkin ten- sor, Lagrange-Laplace-Runge-Lenz vector, Fradkin-Bacry-Ruegg-Souriau vector, Li
Subjects:Mathematics and Applications
Physics, Optics
ID Code:6585
Deposited By:Alicia PETIT
Deposited On:24 mai 2016 16:21
Dernière modification:24 mai 2016 16:21

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