I am looking for textbooks and or lecture notes that give a nice treatment to the time-dependent harmonic oscillator:
$x''(t) + \omega(t)^2\cdot x(t) = 0.$
Treatments that include step-functions would be appreciated.
Time-dependent Harmonic Oscillator resources?
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ordinary-differential-equations
classical-mechanics
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0Do you have particular question in mind? Many books or lecture notes have the explanation for the case when $\omega(t)$ is a small perturbation of true harmonic oscillator (i.e. $\omega(t) = \omega_0 + \epsilon \omega_1(t) + \epsilon^2 \omega_2(t) + \dots$), so called Poincare-Lindstedt method. The case when $\omega(t)$ is somehow related to step functions is exactly solvable by means of general linear equations theory, so I am not sure that I get your question right. – 2017-02-28
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0Yes, I have been (embarrassingly) reminded of the step function solution. I am hoping to find a more general theory... I will look up the Poincare-Lindstedt method that you have listed, but I am wondering about any analytic solutions that exist, and or methods of finding them (such as the one you listed). – 2017-03-14
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0Well, PL method is the suitable method then. I suggest you just skim table of contents of books on nonlinear dynamics that you have access to :) – 2017-03-15