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The orbital resonance amongst the Galilean satellites of Jupiter
Springer Science and Business Media LLC - Tập 12 - Trang 89-96 - 1975
The resonance amongst three of the Galilean satellites is described in a way intended to demonstrate the similarities it has to the normal two-satellite resonance. The hypothesis that the resonance was formed by the action of tidal forces is discussed. The problem is too complicated to reach any firm conclusions, but the tidal hypothesis does not seem to be a satisfactory explanation.
Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite
Springer Science and Business Media LLC - Tập 3 - Trang 346-383 - 1971
Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rig......
Planetary encounter analysis on the B-plane: a comprehensive formulation
Springer Science and Business Media LLC - - 2019
A numerical investigation of the one-dimensional Newtonian three-body problem
Springer Science and Business Media LLC - Tập 51 - Trang 379-394 - 1991
The one-dimensional Newtonian three-body problem is known to have stable (quasi-)periodic orbits when the masses are equal. The existence and size of the stable region is discussed here in the case where the three masses are arbitrary. We consider only the stability of the periodic (generalized) Schubart's (1956) orbit. If this orbit is linearly stable it is almost always surrounded by a region of......
Deprit’s reduction of the nodes revisited
Springer Science and Business Media LLC - Tập 109 - Trang 285-301 - 2011
We revisit a set of symplectic variables introduced by Andre Deprit (Celest Mech 30, 181–195, 1983), which allows for a complete symplectic reduction in rotation invariant Hamiltonian systems, generalizing to arbitrary dimension Jacobi’s reduction of the nodes. In particular, we introduce an action-angle version of Deprit’s variables, connected to the Delaunay variables, and give a new hierarchica......
A note on resonance in regular variables and averaging
Springer Science and Business Media LLC - Tập 34 - Trang 453-457 - 1984
A point relative to the application of the method of Hori to resonant systems is considered: For systems having one degree of freedom the topology of the phase plane of the auxiliary Hori's system is unaltered in the process of construction of a formal solution. The transformed Hamiltonian may not lead to singular points other than those included in the auxiliary Hori's Hamiltonian.
Wavelet analysis and applications to some dynamical systems
Springer Science and Business Media LLC - Tập 56 - Trang 231-262 - 1993
For about five years the wavelet transform technique has given interesting results in a great number of different fields such as mathematics, quantum mechanics, signal analysis and image processing, cluster analysis... The wavelet transform appears as a new time-frequency method which is particularly well-suited to detect and to localize discontinuities and scaling behaviours in signals. The main ......
Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for Their Origins
Springer Science and Business Media LLC - Tập 78 - Trang 93-112 - 2000
The population of Near-Earth Asteroids (NEAs) appears to be overabundant at sizes smaller than 50 m, compared to a power-law extrapolation from kilometer-sized objects. Several of these small NEAs are also concentrated on low-eccentricity orbits, where a few larger Earth-crossers are observed, and are called Small Earth-Approachers (SEAs). Their source region as well as the dynamical mechanisms in......
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