Search

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Àngel Jorba i Monte, [en] The mechanics of celestial bodies has been studied since the origin of human reasoning, specially the planets. We have seen examples of this in the counting of lunar cycles of the primitive homo sapiens, the stars dome of the greek, or in the geocentric and heliocentric visions of our Solar system. Nowadays, with all the avances in the fields of Maths, modern Physics and computers, the study of celestial bodies mechanics has advanced a lot. This paper aims to explain the behaviour of big mass particles attracted to each other in space, according to the laws of Keppler and Newton. This is carried out from a modern point of view and with mathematical rigor.

We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k , n)-crown. We derive the equations of central configurations for a general ( k, n)-crown. When k = 2 we prove the existence of a twisted (2, n)-crown for any value of the mass ratio. Moreover, for n = 3, 4 and any value of the mass ratio, we give the exact number of twisted (2, n)-crowns, and describe their location. Finally, we conjecture that for any value of the mass ratio there exist exactly three (2; n)-crowns for n>=5 The authors are supported by MINECO grants MTM2016-80117-P and MTM2016-77278-P (FEDER) and Catalan (AGAUR) grants 2017 SGR 1374 and 2017 SGR 1617

Made available in DSpace on 2018-12-11T17:26:44Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-01 In this work, we are interested in avoiding large variations in the mutual distances among multiple satellites and also in controlling their geometric configuration around an Earth-Moon triangular point. Previous studies about triangular libration points have determined the existence of zero drift regions with respect to the nominal trajectory, in which the expansion or contraction of the formation never take place. Our goal is to carry out two different control strategies for a formation near a given nominal trajectory around L4: a bang-off-bang control and a minimum weighted total ΔV consumption. A linearization relative to the reference trajectory around the triangular libration point is carried out, and different geometrical possibilities in the zero drift regions are studied. To investigate the influence of the gravitational force of the Sun, the BiCircular Four Body Problem is considered here. According to the results obtained, some meaningful insights to allow a proper design of the geometric configuration of the formation are drawn. UNESP-Grupo de Dinâmica Orbital e Planetologia Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758 Departament de Matemàtica Aplicada i ETSEIB-UPC, Avda. Diagonal 647 Departament de Matemàtica Aplicada i Anàlisi UB, Gran Vía 585 UNESP-Grupo de Dinâmica Orbital e Planetologia