Celestial Mechanics: Analytical and Numerical Methods and Applications
Type of activity
AGENCIA ESTATAL DE INVESTIGACION
Funding entity code
The project is born from a series of recent developments in Celestial Mechanics (CM) achieved by several members of the UPC Dynamical Systems Group in dynamical systems. It brings together researchers from the UPC, the UdG and the UNIR, with an increasing experience in these areas with a important interaction between them. The main purpose is to apply the analytical and numerical tools developed for general dynamical systems to problems in Astrodynamics, CM and related applications, like several problems of atomic dynamics. The questions span from obtaining high accuracy satellite orbits and transfer dynamics, in Astrodynamics, to more general questions in CM: the existence of transport, chaos and connecting orbits in several instances of the N-body problem, as well as the computation of particular solutions of those problems. Our proposal combines analytical techniques, numerical explorations, combination of rigorous analytical parts based on an ansatz that is checked numerically and computer assisted proofs. Computer computations require the use of our HPC cluster. The specific goals are: Research line 1. Oscillatory orbits. Goal 1.1. Atomic physics. Chaos in atom-surface scattering. Goal 1.2. Oscillatory orbits in the planar three body problem (3BP). Research line 2. Transfer Dynamics Involving Libration Point Regimes. Goal 2.1. Solar sail manoeuvres (I). Goal 2.2. Solar sail manoeuvres (II). Goal 2.3. Solar sail manoeuvres (III). Research line 3. Transport, diffusion and invariant objects in finite dimensional systems. Goal 3.1. Atomic physics: the CP problem. Goal 3.2. Arnold diffusion along mean motion resonances. Goal 3.3. Random models in the restricted planar elliptic 3BP (R3BP). Goal 3.4. Chaotic motions in Hyperion-Saturn system. Goal 3.5. Homo-heteroclinic orbits to libration points in the spatial R3BP. Goal 3.6. Parabolic whiskered tori in the nBP. Goal 3.7. Heteroclinic orbits in the restricted (N+2)-body problem with Manev repulsion. Goal 3.8. Singularly embedded solitons. Research line 4. High Accuracy State and Parameter Estimation for Satellites. Goal 4.1. Efficient nonlinear methods and geostationary trajectories. Goal 4.2. Nonlinear filtering algorithms for orbit determination. Goal 4.3. Parameter estimation and sensitivity analysis. Research line 5. Diffusion in higher dimensions. Goal 5.1. Non transversal shadowing and growth of Sobolev norms. Goal 5.2. Growth of Sobolev norms in the beam equation. Research line 6. Systems with impacts and non-smooth dynamics. Goal 6.1. Periodic orbits and collisions in the collinear 4BP. Goal 6.2. Ejection orbits in the collinear 4BP. Goal 6.3. Ejection-collision orbits (ECO) in the R3BP. Goal 6.4. ECO in general Hamiltonian systems. Goal 6.5. Aging systems and nonlinear regularization of non-smooth systems. Research line 7. Central configurations. Goal 7.1. Aligned and rotated CC. Goal 7.2. Are there non-convex SCC in the 5BP? Research line 8. CM and geometry. Goal 8.1. KAM theory with b3 structures in the R3BP close to parabolic motions. Goal 8.2. b3 structures and triple collisions in the 3BP. Goal 8.3. Symplectic geometry and topology applied to windows and shadowing.