Talk:Kapitza's pendulum

Referral to a figure that doesn't exist
Under the phase portrait section, there is a sentence referring to a figure that is not on the page. While it would be easy to remove this reference, the page itself would benefit greatly from a phase portrait.

"Increasing the amplitude of driving oscillations to half of the pendulum length {\displaystyle a=l/2} a=l/2 leads to the phase portrait shown in the figure."

Lagrangian Derivation
The derivation of the Lagrangian seems to be incorrect. Either I am mistaken, or there should be a negative term: L=m/2 l^2 〖θ'〗^2 +mlgcos(θ)-malv^2sin(θ)sin(vt). The last term is positive in the article right now. Upon checking other calculations of the Kapitza pendulum, it seems this article reaches the same result, but it is unclear in this article whether or not a negative was simply dropped. 198.82.125.252 (talk) 07:33, 7 May 2015 (UTC)

External links modified
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Kapitza wasn't the first to analyze Kapitza pendulum
You can find a proof that a pendulum with a vibrating suspension has a stable upright position in a classic textbook of mathematical methods: Harold Jeffreys and Bertha Swirles Jeffreys. Methods of Mathematical Physics. 2nd ed. Cambridge University Press, 1950. Chap. Solution of Linear Differential Equations of the Second Order, pp. 488–489. Moreover, Kapitza in his paper honestly cites this book. Patulus (talk) 05:23, 20 August 2023 (UTC)