Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

7

Circular Orbits, Equations Of Motion, Orbital Mechanics, Periodic Functions, Three Body Problem, Collinearity, Numerical Integration, Variational Principles

Scientific paper

The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies 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 Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-1441230

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.