On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body
2020, Vol. 16, no. 4, pp. 581-594
Author(s): Bardin B. S.
A method is presented of constructing a nonlinear canonical change of variables which
makes it possible to introduce local coordinates in a neighborhood of periodic motions of an
autonomous Hamiltonian system with two degrees of freedom. The problem of the orbital stability
of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov
case is discussed as an application. The nonlinear analysis of orbital stability is carried out
including terms through degree six in the expansion of the Hamiltonian function in a neighborhood
of the unperturbed periodic motion. This makes it possible to draw rigorous conclusions
on orbital stability for the parameter values corresponding to degeneracy of terms of degree four
in the normal form of the Hamiltonian function of equations of perturbed motion.
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