Theorem of Optimal Image Trajectories in the Restricted Problem of Three Bodies View Full Text


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Article Info

DATE

2015-12-09

AUTHORS

Mauro Pontani, Angelo Miele

ABSTRACT

The restricted three-body problem represents the dynamical framework employed for spacecraft mission analysis, in the presence of two attracting bodies, since the 1950s. In this context, orbital motion is often chaotic, although several special solutions (equilibrium points, periodic orbits, and quasiperiodic trajectories) exist, and can be—or have already been—profitably employed in space missions. The theorem of image trajectories, proven five decades ago by Miele, states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits), there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and proved extremely useful for investigating the natural dynamics in the restricted problem of three bodies, by identifying special solutions, such as symmetric periodic orbits and free return trajectories. This work extends the theorem of image trajectories to optimal paths, which minimize either the propellant consumption or the time of flight, by determining the relations between the optimal thrust sequence, magnitude, and direction of an outgoing path and a symmetrical returning trajectory. This means that while the theorem of image paths revealed extremely useful for investigating natural dynamics, the theorem of optimal image trajectories can be profitably employed for powered orbital motion, i.e., in the context of impulsive and finite-thrust orbit transfers and rendezvous, as well as for the purpose of analyzing artificial periodic orbits that use very low thrust propulsion. More... »

PAGES

992-1013

References to SciGraph publications

  • 1984-01. Three-dimensional, periodic, ‘halo’ orbits in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1998-06. Quasihalo Orbits Associated with Libration Points in THE JOURNAL OF THE ASTRONAUTICAL SCIENCES
  • 2012-11-16. Periodic Image Trajectories in Earth–Moon Space in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2003-03. New Families of Periodic Orbits in Hill's Problem of Three Bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2010-07-24. Revisit of the Theorem of Image Trajectories in the Earth-Moon Space in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1980-10. Analytic construction of periodic orbits about the collinear points in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1987-03. Numerical determination of Lissajous trajectories in the restricted three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973-02. General theory of optimal trajectory for rocket flight in a resisting medium in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1979-11. The ‘Halo’ family of 3-dimensional periodic orbits in the Earth-Moon restricted 3-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1897. Periodic Orbits in ACTA MATHEMATICA
  • 1973-06. Quasi-periodic orbits about the translunar libration point in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2011-10-26. Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2003. Optimal Control Theory for Applications in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10957-015-0852-3

    DOI

    http://dx.doi.org/10.1007/s10957-015-0852-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046745674


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