Improbability of Collisions in n-Body Systems

For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in n -body systems are of Liouville measure zero for all energies. We use techniques from symplectic geometry to relate the volume of the union of collision orbi...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2019-12, Vol.234 (3), p.1007-1039
Main Authors: Fleischer, Stefan, Knauf, Andreas
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Orbits
Physics
Physics and Astronomy
Theoretical
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Summary:For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in n -body systems are of Liouville measure zero for all energies. We use techniques from symplectic geometry to relate the volume of the union of collision orbits to the area of Poincaré surfaces surrounding the collision set.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-019-01406-4