On the motion of non-linear oscillators with a fractional-order restoring force and time variable parameters
On the motion of non-linear oscillators with a fractional-order restoring force and time variable parameters
An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov–Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results
slow time, fractional-order restoring force, variational principle, uncommutative rule, krylov–bogoliubov method
1839-1843
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
4 May 2009
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Kovacic, Ivana
(2009)
On the motion of non-linear oscillators with a fractional-order restoring force and time variable parameters.
Physics Letters A, 373 (21), .
(doi:10.1016/j.physleta.2009.03.046).
Abstract
An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov–Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results
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Published date: 4 May 2009
Keywords:
slow time, fractional-order restoring force, variational principle, uncommutative rule, krylov–bogoliubov method
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Local EPrints ID: 79128
URI: http://eprints.soton.ac.uk/id/eprint/79128
ISSN: 0375-9601
PURE UUID: 6952adc0-f3a9-44ca-bf65-1c579621402e
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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 00:28
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Author:
Ivana Kovacic
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