Other
Scientific paper
Aug 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003basbr..23..242c&link_type=abstract
Boletim da Sociedade Astronômica Brasileira (ISSN 0101-3440), vol.23, no.1, p. 242-243
Other
Scientific paper
The simplicity of the three body problem in its various forms has attracted the attention of mathematicians for centuries. Among the giants of mathematics who have tackled the problem and made important contributions are Euler, Lagrange, Laplace, Jacobi, LeVerrier, Hamilton and Poincaré. Szebehely's (1967) book provides an important coverage of the literature on the subject as well as derivations of important results. When the third body is too small to affect the motion of the other two bodies, the problem of the motion of the third body is called the restricted three body problem. In the restricted three body problem, the motion of the primaries must satisfy the differential equations that describe the dynamics of two gravitational bodies. Consequently, the primaries might describe elliptic, parabolic or hyperbolic orbits. The case, when the primaries move on circles, gives a general definition to simplify its development. However, it is a particular case and to carry out a more realistic study, elliptical motion of the primaries must be introduced. The generalization of this case is not trivial: while the restricted circular problem of three bodies still possesses the jacobi integral, the elliptic problem does not. This property of the elliptic problem distinguishes it from the circular problem and indicates the increased degree of difficulty involved in solving it. The circular problem presents the well known lagrangian equilibrium points. Due to the structure of the phase space there are two families of stable coorbital orbits known as tadpole and horseshoe. The main objective of the present study is to evaluate how the effects of the eccentricity of the primaries can affect the stability of these coorbital trajectories. Therefore, in this study we show how the elliptic problem can be formulated and numerical simulations are made using the pulsating coordinates system to determine how the eccentricity of the primaries orbits change the stability of horseshoe and tadpole orbits. Our results show that the amplitude of oscillation increases for orbits around L4 and decreases for orbits around L5.
Cabo Winter Othon
Chanut G. G. T.
Tsuchida Masayoshi
No associations
LandOfFree
Dynamics of coorbital systems in the planar elliptic case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dynamics of coorbital systems in the planar elliptic case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of coorbital systems in the planar elliptic case will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1666131