Nonsemisimple 1∶1 resonance at an equilibrium

Details Nonsemisimple 1∶1 resonance at an equilibrium Nonsemisimple 1∶1 resonance at an equilibrium

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27..131v&link_type=abstract

Celestial Mechanics, Volume 27, Issue 2, pp.131-149

Computer Science

7

Scientific paper

Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesiα,iα,-iα,-iα (α ∈ ℝ, α>0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL 4 the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated.

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