Physics
Scientific paper
Sep 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986zamp...37..776h&link_type=abstract
Zeitschrift für angewandte Mathematik und Physik (ISSN 0044-2275), vol. 37, Sept. 1986, p. 776-796.
Physics
13
Asteroids, Hyperbolic Trajectories, Orbital Mechanics, Orbital Resonances (Celestial Mechanics), Solar Orbits, Dissipation, Gravitational Effects, Hamiltonian Functions, Invariance, Jupiter (Planet), Two Body Problem
Scientific paper
An algebraic mapping is found which contains all the properties of the dynamical system which describes the motion of an asteroid in the Sun-Jupiter system, in the restricted circular 3-body problem, near the 3:1 resonance. The mapping is constructed by starting from the corresponding mapping of the two body problem, sun-asteroid, in a rotating frame (twist mapping) and then by including the main effect of Jupiter, which is obtained analytically to be the generation of instabilitay (hyperbolic mapping). The product of these two mappings is a hyperbolic twist mapping which gives invariant curves close to the actual case. This latter mapping depends on the energy, as a parameter. The properties of this mapping are studied, in connection with evolution of an asteroid oribt which passes through the 3:1 resonance due to a particular mode of energy dissipation.
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