Abstract
We saw in Fig. 11.3b that if the frequency ω p of the change in the system’s parameter is much smaller than the fundamental frequency ω 0 (ω p ≪ ω 0)), then there is practically no instability. The instability zone becomes narrower as the ratio ω 0 /ω p) increases. This case of a very slow, adiabatic, change in the parameter (of which an example is the oscillation of a pendulum whose length is changing slowly) is very interesting for a discussion of oscillations and waves, and at the same time it is often encountered in practice.
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Rabinovich, M.I., Trubetskov, D.I. (1989). Adiabatic Invariants. Propagation of Waves in Inhomogeneous Media. In: Oscillations and Waves. Mathematics and Its Applications (Soviet Series), vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1033-1_12
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DOI: https://doi.org/10.1007/978-94-009-1033-1_12
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