ある非線型振動の全ての分数調波解

概要

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In the last volume, the author has shown that the fundamental and the several subharmonic (for instance 1/2, 1/3, ……etc) solutions exist in nonlinear oscillations which are generated in a series circuit of a resistance, an inductance and a capacitance with an alternating electromotive force, where the value of the resistance and the value of the capacitance are always constant, but the value of ψ (the magnetic flux interlinkage of the inductance) is -ψ_m if i (the electric current) < 0, the value of ψ is ψ_m if i > 0 and ψ takes the value between -ψ_m and ψ_m if i = 0. And it was shown that there are some subharmonics with different modes in the same kind of subharmonic solutions. In this report, the anthor introduces an index representation for an arbitrary periodic solution and by this representation it is shown that there is not any different mode about 1/2 and 1/3 subharmonics except for the modes as shown in the last volume. And all modes of 1/4 subharmonics are shown by this index representation.
明治大学の論文