ある非線型振動モードについて

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We consider a series circuit of a resistance, an inductance and a capacitance with an alternating electromotive force, where the resistance and the capacitance are linear, butΨ', the value of magnetic flux interlinkage in inductance, is the constant value-Ψ_m if the electric current is minus, and also, it is the constant value Ψ_m if the current is plus, and lastly, it takes the value between-Ψ_m and Ψ_m (-Ψ_m≦Ψ≦Ψ_m if the current is zero. We can express this circuit equation by the nonlinear differential equations, and we can obtain the exact solutions on each piecewise-linear section, because, as stated above, its nonlinear characteristic is the piecewise-linear. However, it is very difficult to get the entire picture of that solution because of the different initial conditions on each linear section. In this nonlinear circuit, the author has shown the existence of various periodic solutions (fundamental or subharmonic solutions on stable, metastable, or unstable state) and has made clear the method to change their oscillation domain under the circuit parameters γ, ψ_m, which are normalized quantities of R, Ψ_m. But, at this point, we must pay attention to possibility that there might be different modes in the same subharmonic, for instance 1/2, 1/3, …etc. In this report, at the beginning, fundamental and subharmonic solutions are briefly mentioned and then the modes which exist about some periodic solutions are expressed. Lastly, this report briefly refers to almost periodic solutions which have been disputed in nonlinear problems.
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ある非線型振動モードについて

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