Theorem of Optimal Image Trajectories in the Restricted Problem of Three Bodies

Mauro Pontani () and Angelo Miele
Additional contact information
Mauro Pontani: University “La Sapienza”
Angelo Miele: Rice University

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 15, 992-1013

Abstract: 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.

Keywords: Image trajectories; Theorem of optimal image trajectories; Restricted problem of three bodies; Spacecraft trajectory optimization; 49M05 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0852-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0852-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-015-0852-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().