Tatiana Churkina
Volokolamskoe sh. 4, Moscow, 125993 Russia
Moscow Aviation Institute (National Research University)
Publications:
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Markeev A. P., Churkina T. E.
On the Normal Form of the Hamiltonian in the Vicinity of Lagrange Points in the Restricted Elliptical Three-Body Problem
2026, Vol. 22, no. 2, pp. 291-307
Abstract
The planar restricted problem of three bodies moving under gravitational attraction is considered.
The motions close to the Lagrange libration points are studied. The orbital eccentricity
of the smaller of the two main attracting bodies and their mass ratio are chosen as problem
parameters. A linear canonical transformation that is $2\pi$-periodic in true anomaly is obtained
analytically up to the 4th degree of eccentricity inclusive, which reduces the Hamiltonian function
of the linearized equations of perturbed motion to a real normal form corresponding to two
harmonic oscillators independent of each other. The oscillations frequencies and the coefficients
in the transformation are obtained explicitly in terms of the problem parameters.
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