Talk:Lagrange, Euler, and Kovalevskaya tops

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"(Redirected from Chaplygin's top) ... There are however three famous cases that are integrable ..."

Which is it? if Chaplygin's top is integrable, "three" should be changed to "four." (Or perhaps "three famous cases and one not-so-famous case" ... smiley-face )Jamesdowallen (talk) 19:22, 10 January 2017 (UTC)[reply]

A short introduction to non-integrability would be nice. I think this is entirely due to the KAM torus but am confused about the details. 67.198.37.17 (talk) 20:11, 12 January 2019 (UTC)[reply]

In both the Lagrange and Kovalevskaya tops, the quantity ${\displaystyle n^{2}=n_{1}^{2}+n_{2}^{2}+n_{3}^{2}}$ is given as a conserved quantity. But by definition, the ${\displaystyle n_{i}}$ are just the components of the fixed basis vector ${\displaystyle {\hat {z}}}$ expanded in the dynamical basis ${\displaystyle {\hat {e}}_{i}}$, so I think ${\displaystyle n^{2}=|{\hat {z}}|^{2}\equiv 1}$. Which is a conserved quantity, but is not an interesting conserved quantity, and is not eligible as a conserved quantity for purposes of Arnold–Liouville integrability. If there's a mistake in my understanding I'd be happy to be corrected! Zephyr the west wind (talk) 16:32, 15 July 2023 (UTC)[reply]