The Collision Singularity in a Perturbed N-Body Problem

Details The Collision Singularity in a Perturbed N-Body Problem The Collision Singularity in a Perturbed N-Body Problem

May 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...5..396s&link_type=abstract

Celestial Mechanics, Volume 5, Issue 3, pp.396-406

Mathematics

1

Scientific paper

Consider the perturbedN-body problem Z_k = - γ sumlimits_{mathop {j ne k}limits^{j = 1} }^N {{Z_k - Zj}/{|Z_k - Zj|^3 }} + P_k ,{text{ }}k = 1,{text{ }}...,N, and assume that at the instantt * allN bodies collide, while theP k remain bounded. It is shown that the motion prior to the instant of collision is essentially the same as in the unperturbedN-body problemP k =0, i.e., the same asymptotic relations are valid in both cases ast→t *.

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