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Exact solution of a triaxial gyrostat with one rotor
The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of
Linearization: Laplace vs. Stiefel
The method for processing perturbed Keplerian systems known today as the linearization was already known in the XVIIIth century; Laplace seems to be the first to have codified it. We reorganize the
Frozen Orbits About the Moon
Frozen orbits are of special interest to mission designers of artificial satellites. On average the eccentricity and argument of the perigee of such orbits remain stationary. Frozen orbits correspond
The Lissajous transformation II. Normalization
Normalization of a perturbed elliptic oscillator, when executed in Lissajous variables, amounts to averaging over the elliptic anomaly. The reduced Lissajous variables constitute a system of
A simple model for the chaotic motion around (433) Eros
The three-dimensional motion in the close vicinity of Asteroid 433 Eros is known to be chaotic for a wide range of inclinations. This asteroid is potato-shaped, clearly distinct from an oblate body
Analytical Model to Find Frozen Orbits for a Lunar Orbiter
Analytical theories based on Lie-Deprit transforms are used to obtain families of periodic orbits for the problem of an orbiter around the moon. Low and moderately high orbit models are analyzed.
Attitude dynamics of a rigid body on a Keplerian orbit: A simplification
An infinitestimal contact transformation is proposed to simplify at first order the Hamiltonian representing the attitude of a triaxial rigid body on a Keplerian orbit around a mass point. The
Periodic Orbits Around a Massive Straight Segment
In this paper, we consider the motion of a particle under the gravitational field of a massive straight segment. This model is used as an approximation to the gravitational field of irregular shaped