Характеристические показатели периодических решений гамильтоновых систем…
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Characteristic exponents of periodic solutions of Hamiltonian
systems and the necessary conditions of stability
© A.A. Pankratov
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article considers Hamiltonian system with a small parameter (the main task of the
dynamics in the terminology of Poincare). The structure of the decomposition of the
characteristic exponents of periodic solutions in series in integer and fractional powers
of the small parameter was investigated. The main members in these decompositions are
obtained, necessary stability conditions of periodic decisions were found.
Keywords:
Hamiltonian system, the Poincare method, periodic and quasi-periodic mo-
tions, characteristic exponents, stability.
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Pankratov A.A.
(b. 1952) graduated from the mechanics and mathematics faculty of
Lomonosov Moscow State University in 1974. Ph.D., assoc. professor of the Department
of Theoretical Mechanics at Bauman Moscow State Technical University. The author of
more than 60 works in the dynamics of solid body, of analytical mechanics and applied
celestial mechanics.
e-mail:
