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Title: A Note on an Existence of Conditionally Periodic Oscillation in a one-dimensional Anharmonic Lattice
Authors: NISHIDA, Takaaki
Issue Date: 31-Mar-1971
Publisher: Faculty of Engineering, Kyoto University
Journal title: Memoirs of the Faculty of Engineering, Kyoto University
Volume: 33
Issue: 1
Start page: 27
End page: 34
Abstract: The oscillations of a one-dimensional anharmonic lattice is investigated sufficiently near the equilibrium state, which is described by the equation d²yᵢ/dt²=y₊₁-2yᵢ+yᵢ₋₁+α{(yᵢ₊₁-yᵢ)³-(yᵢ-yᵢ₋₁)³}, -∞<t<+∞, where i=1, 2, ・・・ n, α=constant, boundary conditions are y₀=yₙ₊₁=O and initial conditions yᵢ(0), dyᵢ(O)/dt are given. A large part of the oscillations starting from initial data sufficiently near the origin of the phase space of the system is proved to be a conditionally periodic motion under the incommensurable condition on linear frequencies mentioned later.
URI: http://hdl.handle.net/2433/280840
Appears in Collections:Vol.33 Part 1

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