Masses for which Triple Collision is Regularizable

Details Masses for which Triple Collision is Regularizable Masses for which Triple Collision is Regularizable

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21...25s&link_type=abstract

Celestial Mechanics, Volume 21, Issue 1, pp.25-36

Statistics

Computation

10

Scientific paper

We consider the regularization by continuity w.r.t. initial conditions (geometric or Easton method) which has a sense both in physical and computational aspects. Using the idea of triple collision manifold of McGehee we study the values of masses for which the invariant manifolds of equilibrium points coincide. Local analytical equations are continuated numerically. So one gets the masses satisfying a necessary condition. Again analytically we discuss the neighbourhood of t.c.m. at the equilibrium points. A necessary and sufficient condition in terms of integrals along invariant manifolds is found for the rectilinear case. This can be tested for the masses obtained above. Only a countable (symmetric) set of masses remains. Then, due to errors in physical measurements or numerical integrations we can never expect a regular behaviour. Extension to the planar case is also taken into account.

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