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In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the(More)
There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by Europa presents formidable challenges to traditional conic analysis since the regimes of motion involved depend heavily on three-body dynamics. New three-body(More)
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material(More)
This paper concerns heteroclinic connections and resonance transitions in the planar circular restricted 3-body problem, with applications to the dynamics of comets and asteroids and the design of space missions such as the Genesis Discovery Mission and low energy Earth to Moon transfers. The existence of a heteroclinic connection between pairs of equal(More)
The TPF Mission (Terrestrial Planet Finder) is one of the center pieces of the NASA Origins Program. The goal of TPF is to identify terrestrial planets around stars nearby the Solar System. For this purpose, a space-based infrared interferometer with a baseline of approximately 100 m is required. To achieve such a large baseline, a distributed system of(More)
In recent years, increasing evidence indicating numerous health benefits associated with the intake of probiotic bacteria has created a big market of probiotic foods worldwide. However, maintaining high numbers of viable cells in probiotic food products during the shelf life of the product and during gastrointestinal transit is a challenge. The goal of this(More)
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks(More)
We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near the 3:2 Hilda resonance into the realm of orbits crossing Mars' orbit are computed. In contrast to common numerical approaches, our technique does not depend on(More)
To Henri Poincaré on the 150th anniversary of his birth. Abstract. The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three body problem. Since then, many researchers have contributed to his legacy by developing and applying(More)