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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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