Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism
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Дата
2016
Автори
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
NTU "KhPI"
Анотація
Over recent years, a lot of progress has been achieved in understanding of the relationship between
localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to
demonstrate that the structure of the resonance manifold can be conveniently described in terms of canonical
action-angle variables. Such formalism has important theoretical advantages: all resonance manifolds may be
described at the same level of complexity, appearance of additional conservation laws on these manifolds is
easily proven both in autonomous and non-autonomous settings. The harmonic balance - based
complexification approach, used in many previous studies on the subject, is shown to be a particular case of
the canonical formalism. Moreover, application of the canonic averaging allows treatment of much broader
variety of dynamical models. As an example, energy exchanges in systems of coupled trigonometrical and
vibro-impact oscillators are considered.
Опис
Ключові слова
energy transport, strong nonlinearity, canonical variables
Бібліографічний опис
Gendelman O. V. Energy Exchange and Localization in Essentially Nonlinear Oscillatory Systems: Canonical Formalism / O. V. Gendelman, T. Sapsis // Nonlinear Dynamics–2016 (ND-KhPI2016) : proceedings of 5th International Conference, dedicated to the 90th anniversary of Academician V. L. Rvachev, September 27-30, 2016 = Нелінійна динаміка–2016 : тези доп. 5-ї Міжнар. конф., 27-30 вересня 2016 р. – Kharkov : NTU "KhPI", 2016. – P. 82-91.