27 research outputs found
A first-order secular theory for the post-Newtonian two-body problem with spin -- I: The restricted case
We revisit the relativistic restricted two-body problem with spin employing a
perturbation scheme based on Lie series. Starting from a post-Newtonian
expansion of the field equations, we develop a first-order secular theory that
reproduces well-known relativistic effects such as the precession of the
pericentre and the Lense-Thirring and geodetic effects. Additionally, our
theory takes into full account the complex interplay between the various
relativistic effects, and provides a new explicit solution of the averaged
equations of motion in terms of elliptic functions. Our analysis reveals the
presence of particular configurations for which non-periodical behaviour can
arise. The application of our results to real astrodynamical systems (such as
Mercury-like and pulsar planets) highlights the contribution of relativistic
effects to the long-term evolution of the spin and orbit of the secondary body.Comment: 14 pages, 3 figures, Published in MNRA
Analytical perturbative theories of motion in highly inhomogeneous gravitational fields : Ariadna AO/1-6790/11/NL/CBI
In this report we show that modern computer performances and state-of-the-art algebraic manipulator software are sufficiently developed to carry out our generalised analytical perturbative theory. This report addresses three technical aspects to develop a general perturbative theory and illustrates its power by applying it to investigate the inhomogeneous gravitational fields of asteroids
Differentiable Genetic Programming
We introduce the use of high order automatic differentiation, implemented via
the algebra of truncated Taylor polynomials, in genetic programming. Using the
Cartesian Genetic Programming encoding we obtain a high-order Taylor
representation of the program output that is then used to back-propagate errors
during learning. The resulting machine learning framework is called
differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic
regression, dCGP offers a new approach to the long unsolved problem of constant
representation in GP expressions. On several problems of increasing complexity
we find that dCGP is able to find the exact form of the symbolic expression as
well as the constants values. We also demonstrate the use of dCGP to solve a
large class of differential equations and to find prime integrals of dynamical
systems, presenting, in both cases, results that confirm the efficacy of our
approach
A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation
A software platform for global optimisation, called PaGMO, has been developed
within the Advanced Concepts Team (ACT) at the European Space Agency, and was
recently released as an open-source project. PaGMO is built to tackle
high-dimensional global optimisation problems, and it has been successfully
used to find solutions to real-life engineering problems among which the
preliminary design of interplanetary spacecraft trajectories - both chemical
(including multiple flybys and deep-space maneuvers) and low-thrust (limited,
at the moment, to single phase trajectories), the inverse design of
nano-structured radiators and the design of non-reactive controllers for
planetary rovers. Featuring an arsenal of global and local optimisation
algorithms (including genetic algorithms, differential evolution, simulated
annealing, particle swarm optimisation, compass search, improved harmony
search, and various interfaces to libraries for local optimisation such as
SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs
an object-oriented architecture providing a clean and easily-extensible
optimisation framework. Adoption of multi-threaded programming ensures the
efficient exploitation of modern multi-core architectures and allows for a
straightforward implementation of the island model paradigm, in which multiple
populations of candidate solutions asynchronously exchange information in order
to speed-up and improve the optimisation process. In addition to the C++
interface, PaGMO's capabilities are exposed to the high-level language Python,
so that it is possible to easily use PaGMO in an interactive session and take
advantage of the numerous scientific Python libraries available.Comment: To be presented at 'ICATT 2010: International Conference on
Astrodynamics Tools and Techniques