Elimination des noeuds dans le probleme newtonien des quatre corps View Full Text


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Article Info

DATE

1982-08

AUTHORS

Françoise Boigey

ABSTRACT

We apply the method of canonical trasformations with imposed variables to the reduction of the Newtonian four-body problem. After the elimination of the center of gravity, the problem is reduced to that of three fictitious bodies. Then we proceed to the actual reduction using the integrals of angular momentum, in Hamiltonian formulation, and considering the geometrical aspects of the elimination of the nodes advocated by Jacobi.We impose three functions as new variables: the third integral of angular momentum and two invariant functions; these last two functions will remain null when we take as third coordinate axis the axis, defined by the momentum vector of the four bodies; they are chosen in involution with the third integral of momentum and so that their Poisson bracket is equal to one. Then we determine a system of fourteen canonical variables which have a simple geometrical interpretation. It is an actual elimination of the nodes: a pseudonode for the second and third fictitious bodies is introduced which coincides with the node of the first fictitious body; the node and the pseudo-node are referred to by an ignorable parameter. More... »

PAGES

399-414

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01228562

DOI

http://dx.doi.org/10.1007/bf01228562

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1050473829


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