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A canonical reduction of order for the Kepler problem

S E Godfrey and G E Prince

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Using a new reduction of order technique the authors obtain four conserved quantities of the classical planar Kepler problem via the symmetries of the equations of motion and an extra vector field. By passing to a suitable quotient manifold of the evolution space they deduce that negative energy orbits are closed and periodic, without having to solve the differential equation.


PACS

45.50.Pk Celestial mechanics

02.30.Jr Partial differential equations

MSC

70G65 Symmetries, Lie-group and Lie-algebra methods

35Gxx General higher-order equations and systems

70F15 Celestial mechanics

Subjects

Mathematical physics

Astrophysics and astroparticles

Dates

Issue 23 (7 December 1991)



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