tag:blogger.com,1999:blog-7729093380675162051.post5486214141562648743..comments2017-06-23T14:09:57.407+10:00Comments on moyhu: World map projection using cubed sphereNick Stokeshttps://plus.google.com/103029875534779648576noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7729093380675162051.post-14182221430009579042017-06-23T14:09:57.407+10:002017-06-23T14:09:57.407+10:00Yes, that is a good way of doing it. Anything that...Yes, that is a good way of doing it. Anything that is topologically equivalent to a sphere can more easily have the right natural frequency behaviour. <br />Nick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-69428757133329834872017-06-23T03:50:42.163+10:002017-06-23T03:50:42.163+10:00What's interesting about these kind of spheric...What's interesting about these kind of spherical transformations is that they can significantly simplify problem solving. I have an example of simplifying Laplace's derivation of the primitive equations along the equator here:<br /><br /><a href="http://contextearth.com/compact-qbo-derivation/" rel="nofollow">http://contextearth.com/compact-qbo-derivation/</a><br /><br />The realization of the earth's equatorial latitude (phi) varying due to the mutual interaction with the nodal orbit of the moon and sun provides a huge simplification to the equations. This is what amounts to a clever ansatz defining the time-varying equatorial path with the greatest lines of attractive force. If one applies this simplification, Laplace's tidal equations reduce to a closed-form analytical solution. If one doesn't simplify, the equations remain underdetermined and difficult to deal with. And I think that's why they can't make sense of behaviors such as QBO.<br /><br />That being said, the issue that I am certain people will have with this formulation is that it appears that it's fiddling with the space-time continuum by having one of the spherical rotational axes (the latitude) vary with time. That makes it qualitatively similar to the Lorentz transformation. I don't necessarily have a ideal answer for this other than how it may help to understand the observed dynamics. By allowing the equatorial latitude to slightly vary in cyclic fashion, is the simplification worth the understanding we get from this formulation? <br />@whuthttp://www.blogger.com/profile/18297101284358849575noreply@blogger.com