This course is composed of two parts, with an equivalent number of hours.
Orbital dynamics part:
The recent advent of nanosatellites, the announcement of new mega-constellations of satellites including thousands of units, along with the contemporary awareness of the risk posed by space debris, have all in common the need to understand the behavior of bodies in orbit around Earth, in the short and long-term range. This issue falls under a field called astrodynamics, or more generally orbital dynamics. This domain being a branch of celestial mechanics possesses therefore a long history, and proceeds from dynamical systems theory and analytical mechanics in its mathematical and physical foundations. It is still an active field of research, with for instance the recent use of tools stemming from chaos theory to study the long-term stability of orbits: we can mention the computations of chaos indicators in order to determine the best solutions for satellites’ end of life (reentry or graveyard orbits), or also the study of orbital resonances present in some regions of space so that satellites naturally end up reentering. In this part of the class we will study the Hamiltonian formulation of orbital dynamics, the resolution of its equations, either analytically using series expansions, or numerically using specific numerical integration schemes, we will develop the perturbation approach and we will analyze the different orbital perturbations at play, we will take up averaging theory, along with the chaos detection tools previously mentioned, and we will examine a cartography of the dynamics in the different orbital regimes used for Earth orbiting satellites, as well as the management of the space debris problem and the risks of collisions.
Multidisciplinary optimization (MDO) applied to launcher design part:
Aerospace vehicle design is a complex process involving numerous disciplines such as aerodynamics, structure, propulsion and trajectory. These disciplines are tightly coupled and may involve antagonistic objectives that require the use of specific methodologies in order to assess trade-offs between the disciplines and to obtain the global optimal configuration. Generally, there are two ways to handle the system design. On the one hand, the design may be considered from a disciplinary point of view (a.k.a. Disciplinary Design Optimization): the designer of each discipline has to design its subsystem (e.g. engine) taking the interactions between its discipline and the others (interdisciplinary couplings) into account. On the other hand, the design may also be considered as a whole: the design team addresses the global architecture of the space vehicle, taking all the disciplinary design variables and constraints into account at the same time. This methodology is known as Multidisciplinary Design Optimization (MDO). The course draws a panorama of the specific mathematical tools used to handle space vehicle design problem complexity: formulations of the MDO problem, choice of the adapted optimization algorithms, use of machine learning techniques to reduce the computational costs and the integration of high-fidelity simulations, etc.
- Profesor: Chabert Pascal