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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,...

Hydrodynamics of Saturn’s Dense Rings

M. Seiß, F. Spahn (2011)

Mathematical Modelling of Natural Phenomena

The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed...

On the Isoenergetical Non-Degeneracy of the Problem of two Centers of Gravitation

Dragnev, Dragomir (1997)

Serdica Mathematical Journal

* Partialy supported by contract MM 523/95 with Ministry of Science and Technologies of Republic of Bulgaria.For the system describing the motion of a moss point under the action of two static gravity centers (with equal masses), we find a subset of the set of the regular values of the energy and momentum, where the condition of isoenergetical non-degeneracy is fulfilled.

Periodic orbits close to elliptic tori and applications to the three-body problem

Massimiliano Berti, Luca Biasco, Enrico Valdinoci (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses...

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