On quasiperiodic perturbations of ordinary differential equations

• Autores: Àngel Jorba i Monte
• Directores de la Tesis: Carles Simó (dir. tes.)
• Lectura: En la Universitat de Barcelona ( España ) en 1991
• Idioma: español
• Tribunal Calificador de la Tesis: Carles Perelló i Valls (presid.) , Ernest Fontich Julià (secret.) , Roberto Moriyón Salomón (voc.) , Juan de la Cruz de Solà-Morales i Rubio (voc.) , Amadeu Delshams i Valdés (voc.)
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • In this work we study several topics concerning quasi-periodic time-dependent perturbations of ordinary differential equations. This kind of equations appear as models in many applied problems of Celestial Mechanics, and we have used, as an illustration, the study of the behaviour near the equilateral libration points of the real Earth-Moon system. Let us introduce this problem as a motivation. As a first approximation, suppose that the Earth and Moon arc revolving in circular orbits around � [+]their centre of masses, neglect the effect of the rest of the solar system and neglect the spherical terms coming from the Earth and Moon (of course, all the effects minor than the above mentioned) as the relativistic corrections, must be neglected). With this, we can write the equations of motion of an infinitesimal particle (by infinitesimal we mean that the particle is influenced by the Earth and Moon, but it does not affect them) by means of Newton's Jaw. The study of the motion of that particle is the so-called Restricted Three Body Problem (RTBP). Usually, in order to simplify the equations, the units of length, time and mass are chosen so that the angular velocity of rotation, the sum of masses of the bodies and the gravitational constant are all equal to one. With these normalized units, the distance between the bodies is also equal to one. If these equations of motion are written in a rotating frame leaving fixed the Earth and Moon (these main bodies are usually called primaries), it is known that the system has five equilibrium points. Two of them can be found as the third vertex of equilateral triangles having the Earth and Moon as vertices, and they are usually called equilateral libration points. (...)