en third fictitious bodies interpretation geometrical aspects brackets Elimination des noeuds dans le probleme newtonien des quatre corps articles probleme newtonien des quatre corps 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. actual elimination body momentum first fictitious body vector problem actual reduction system trasformation angular momentum aspects method parameters article geometrical interpretation gravity le probleme newtonien des quatre corps ignorable parameter canonical variables integrals dans le probleme newtonien des quatre corps 399-414 new variables des quatre corps elimination Elimination des noeuds dans le probleme newtonien des quatre corps canonical trasformations Hamiltonian formulation pseudonode four-body problem fictitious body nodes center quatre corps noeuds dans le probleme newtonien des quatre corps reduction newtonien des quatre corps 2022-01-01T18:03 involution variables https://scigraph.springernature.com/explorer/license/ third integral Poisson brackets center of gravity pseudo-node 1982-08-01 des noeuds dans le probleme newtonien des quatre corps invariant functions Jacobi axis https://doi.org/10.1007/bf01228562 momentum vector formulation function simple geometrical interpretation 1982-08 false Corps pub.1050473829 dimensions_id Mathematical Sciences 0008-8714 0923-2958 Celestial Mechanics and Dynamical Astronomy Springer Nature 4 Springer Nature - SN SciGraph project doi 10.1007/bf01228562 Françoise Boigey 27 Institut de Mécanique Théorique et Appliquée, Université P. et M. Curie, Paris Institut de Mécanique Théorique et Appliquée, Université P. et M. Curie, Paris Pure Mathematics