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  • New relative equilibria and their implications in the Full 3-Body Problem (Celestial Mechanics topic)

    Seminar Title  

    New relative equilibria and their implications in the Full 3-Body Problem (Celestial Mechanics topic)

    Speaker:   Prof. Daniel J. Scheeres


    (University of Colorado)  

    When Monday morning, July 10, 10:00 a.m


    Room 202, Astronomy Building

                             Welcome to Attend   

      ( PMO Academic Committee & Academic Circulating committee)

       Abstract: Celestial Mechanics systems have two fundamental conservation principles that enable their deeper analysis: conservation of momentum and conservation of (mechanical) energy. Of the two, conservation of momentum provides the most constraints on a general system, with three translational symmetries (which can be trivially removed) and three rotational symmetries. If no external force acts on the system, these quantities are always conserved independent of the internal interactions of the system. Conservation of energy instead involves assumptions on both the lack of exogenous forces and on the nature of internal interactions within the system. For this reason energy is often not conserved for "real" systems that involve internal interactions, such as tidal deformations or impacts, even though they may conserve their total momentum. Thus mechanical energy generally decays through dissipation until the system has found a local or global minimum energy configuration that corresponds to its constant level of angular momentum.

      This observation motivates a fundamental question for celestial mechanics:
      What is the minimum energy configuration of a N-body system with a fixed level of angular momentum?
      In this talk we show that this is an ill-defined question for traditional point-mass celestial mechanics systems. If instead the system and problem are formulated accounting for finite density distributions this question becomes well posed and provides new light on celestial mechanics systems. We show that this question naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. Applying this theory, we identify new relative equilibria for the finite-density 3-body problem and identify their stability and existence as a function of system angular momentum.
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