Talk:Norton's dome

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Untitled

Note: this article was started from text from the page User:Danski14/prep, created by User:Danski14. -- The Anome (talk) 16:59, 5 August 2014 (UTC)[reply]

Heh, thanks for the attribution, although I only wrote one sentence . My original thinking was to have a page on "non deterministic Netwonian mechanics" because I didn't think the topic of Norton's dome alone was enough for a page. The page you put together looks good though. Great work Danski14^(talk) 20:38, 12 November 2014 (UTC)[reply]

No consensus?

The page states that there is no consensus on how to reconcile Newtonian mechanics with Norton's dome, but reference 6 (http://www.pitt.edu/~jdnorton/Goodies/Dome/) gives a perfectly valid explanation. To that explanation I would only add that Norton's dome has infinite curvature at r=0, and so it is quite obvious that applying the rules valid for masses moving on infinitely smooth surfaces to this dome will give funny results. 144.173.208.87 (talk) 17:14, 13 December 2017 (UTC)[reply]

Lipschitz Continuity

This sentence:

"While many criticisms have been made of Norton's thought experiment, such as it being a violation of the principle of Lipschitz continuity[citation needed],"

should be expanded and modified. I don't know what the "principle of Lipschitz continuity" refers to, but the dynamical system in Norton's dome is markedly not Lipchitz continuous and this is precisely the mathematical reason that it fails to have unique solutions. And it should be perhaps noted that this isn't the first case of nonphysical uniqueness being dealt with by considering physical constraints. For example, the entropy condition used to control shockwave solutions in systems of conservation laws. I think that the phenomenon occurring due to nonuniqueness of solutions and that this is dealt with through physical constraints in other parts of mathematical physics is worth a mention.

For references, any graduate book on ODE will suffice, for example, Jack Hale's Ordinary Differential Equations, or Miller and Michel's Ordinary Differential Equations. For entropy solutions, Evans Partial Differential Equations works. — Preceding unsigned comment added by 23.92.134.163 (talk) 23:02, 21 March 2018 (UTC)[reply]