Martin W. Lo

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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)
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)
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)
Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars.(More)
This paper addresses the computation of the required trajectory correction maneuvers for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the(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)
In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ∆V than a standard Hohmann transfer to the Moon. In this paper, we apply the same dynamical systems techniques used to produce the " Petit Grand Tour " of Jovian moons to reproduce a Hiten-like mission. We decouple the(More)
This paper addresses visualization issues of the Terrestrial Planet Finder Mission[2]. The goal of this mission is to search for chemical signatures of life in distant solar systems using five satellites flying in formation to simulate a large telescope. To design and visually verify such a delicate mission one has to analyze and interact with many(More)
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