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A. C. Clarke's Space Odyssey and Newton's law of gravity

Bartoň, Stanislav, Renčín, Lukáš (2017)

Programs and Algorithms of Numerical Mathematics

In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...

À l'infini en temps fini

Alain Chenciner (1996/1997)

Séminaire Bourbaki

A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.

Jorba, Àngel (1999)

Experimental Mathematics

A theorem for rigid motions in Post-Newtonian celestial mechanics.

J.M. Gambi, P. Zamorano, P. Romero, M.L. García del Pino (2003)

RACSAM

The velocity field distribution for rigid motions in the Born?s sense applied to Post-Newtonian Relativistic Celestial Mechanics is examined together with its compatibility with the Newtonian distribution.

Alternative transfers to the NEOs 99942 apophis, 1994 WR12, and 2007 UW1 via derived trajectories from periodic orbits of family G.

de Melo, C.F., Macau, E.E.N., Winter, O.C. (2009)

Mathematical Problems in Engineering

Applicazioni del teorema di Nekhoroshev alla meccanica celeste

Giancarlo Benettin (2001)

Bollettino dell'Unione Matematica Italiana

The application of Nekhoroshev theory to selected physical systems, interesting for Celestial Mechanics, is here reviewed. Applications include the stability of motions in the weakly perturbed Euler-Poinsot rigid body and the stability of the so-called Lagrangian equilibria $L_{4}$ , $L_{5}$ in the spatial circular restricted three-body problem. The difficulties to be overcome, which require a nontrivial extension of the standard Nekhoroshev theorem, are the presence of singularities in the fiber structure...

Chaotic behaviour in the solar system

Stefano Marmi (1998/1999)

Séminaire Bourbaki

Controlling the eccentricity of polar lunar orbits with low-thrust propulsion.

Winter, O.C., Mourão, D.C., Melo, C.F., Macau, E.N., Ferreira, J.L., Carvalho, J.P.S. (2009)

Mathematical Problems in Engineering

Cruising in a central force field.

Furta, Stanislav, Zampieri, Gaetano (2004)

Portugaliae Mathematica. Nova Série

Das Oszillator-Kepler Problem und die Lie-Algebra.

J. Baumgarte (1978)

Journal für die reine und angewandte Mathematik

Drift and diffusion in phase space

L. Chierchia, G. Gallavotti (1994)

Annales de l'I.H.P. Physique théorique

Dynamique des amas d'étoiles

Michel Hénon (1958/1959)

Séminaire Janet. Mécanique analytique et mécanique céleste

Eight-shaped Lissajous orbits in the Earth-Moon system

Grégory Archambeau, Philippe Augros, Emmanuel Trélat (2011)

MathematicS In Action

Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) $L_{1}, ..., L_{5}$ . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [20, 21, 22, 23, 37]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...