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Symmetry reduction for central force problems

Journal article
Authors R. I. McLachlan
Klas Modin
O. Verdier
Published in European Journal of Physics
Volume 37
Issue 5
ISSN 0143-0807
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Language en
Keywords symplectic reduction, Hamiltonian systems, central force problems, geometrie differentielle, lie, Education & Educational Research, Physics
Subject categories Mathematics, Physical Sciences


We give an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy level sets in three dimensions. These systems form a classic example of symplectic reduction which can usefully be compared to the more commonly seen case of the free rigid body.

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