The circular restricted three-body problem in curvilinear coordinates

We derive the exact equations of motion for the circular restricted three-body problem in cylindrical curvilinear coordinates together with a number of useful analytical relations linking curvilinear coordinates and classical orbital elements. The equations of motion can be seen as a generalization...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2018-11, Vol.130 (11), p.1-16, Article 76
Main Authors: Bombardelli, Claudio, Bernal Mencía, Pablo
Format: Article
Language:English
Subjects:
Aerospace Technology and Astronautics
Astrophysics and Astroparticles
Chaos theory
Circularity
Classical Mechanics
Cylindrical bodies
Cylindrical coordinates
Disturbing functions
Dynamical Systems and Ergodic Theory
Equations of motion
Geophysics/Geodesy
Inclination
Mathematical analysis
Orbital elements
Original Article
Physics
Physics and Astronomy
Three body problem
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Summary:We derive the exact equations of motion for the circular restricted three-body problem in cylindrical curvilinear coordinates together with a number of useful analytical relations linking curvilinear coordinates and classical orbital elements. The equations of motion can be seen as a generalization of Hill’s problem after including all neglected nonlinear terms. As an application of the method, we obtain a new expression for the averaged third-body disturbing function including eccentricity and inclination terms. We employ the latter to study the dynamics of the guiding center for the problem of circular coorbital motion providing an extension of some results in the literature.
ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-018-9870-4