Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals

Details Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals

Sep 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979crasm.289..295b&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie A - Sciences Mathematiques, vol. 289, no. 4, Sept. 17, 1979, p. 295-298. In

Mathematics

1

Canonical Forms, Celestial Mechanics, Four Body Problem, Orbital Mechanics, Transformations (Mathematics), Area, Equations Of Motion, Integral Equations

Scientific paper

The Newtonian four-body problem is reduced to the 14th order by means of canonical transformations with imposed variables, including an area integral. The center of gravity in the problem is eliminated by the introduction of symmetrical variables, reducing the problem to the motion of three fictitious bodies subject to forces deriving from the Newtonian four-body potential in a Hamiltonian formulation. A canonical transformation with the imposition of a variable equal to the third area integral is performed, and a system of two invariant relations is introduced in order to project the angular momentum onto the invariable plane. The successive reductions to fourteenth order, corresponding to node elimination, are then performed by canonical changes in variables and the Jacobi method so that the variables of the reduced problem have a simple geometrical interpretation and permit the explicit calculation of the corresponding Hamiltonian.

Affiliated with

Also associated with

No associations

Rating

Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals 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 Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduction of the Newtonian four-body problem from the 18th to the 14th order by means of area integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1818723