Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2011-10-21
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
24 pages, 7 figures; Accepted for publication in Astrophysics and Space Science
Scientific paper
10.1007/s10509-011-0899-z
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous paper (see \cite{rom11}). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function, we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered in the more massive and the less massive star of the binary system. The 'similar' polar angle's definition is introduced, in order to analyze the regularization's geometrical transformation. The effect of Levi-Civita's transformation is described in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically, for the Earth-Moon binary system.
Roman Rodica
Szucs-Csillik Iharka
No associations
LandOfFree
Regularization of the circular restricted three-body problem using 'similar' coordinate systems 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 Regularization of the circular restricted three-body problem using 'similar' coordinate systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularization of the circular restricted three-body problem using 'similar' coordinate systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-85066