I get something with my GH definition but the final result is missing… Could anybody have a look and tell me where I go wrong ?
Many thanks … GH_Spherical_Harmonics.ghx (225.3 KB)

Hi Ivelin,
No particular reason excep tthat I’m a noob (triyng to impove myself…).
Thank you very much for the answer, I guess you made in seconds what I tried during hours…

It is used a lot to calculate the earth gravity field. So it could represent the geoid (iso gravity surface or mean sea level)
It is mandatory to predict satellites trajectories …

given that the sample illustrations according to Wiki assumes the absence of wind and current, these shapes would never occur in nature? what do the shapes look like if you include wind and currents or is that beyond the scope of the math?

thank you, and as far as an answer to the infinite smoothness problem in the N-S Equations, I solved it: they don’t exist and there is no answer to the problem!

You know, mathematicians are weird breed. When they could not solve some equations with integers, they invented the fractions, when that didn’t work they invented “real” numbers with sign “-” in front, when that didn’t work, they imagined the complex numbers. And when that didn’t work they started inventing multiple (over 3) dimensions to make the number of equations equal the number of unknowns.

I think there is a solution but someone has to imagine or invent something else that doesn’t yet exist.

of course I am joking, I dont have he math skills to even try to prove it but from a distant perch, I sounds similar to other physical events where the math rules apply up to a certain point and then extreme areas of the event, the event descends into chaos.
For example, you may have read or remember the Long-Term Credit Corp collapse where to Nobel laureates in economics had as theory of how to maximize the movement of the credit market. The theory worked 95% of the time, except when the 5% occurred and the market collapsed with a $20B debt. I have a sneaking suspicion that the Boeing 737 problem is related in that the calculations applied in designing the software couldn’t take into account the exponential occurrence of further disruptions. But these are just speculations., I appreciate your suggestion, however. I learned something today…!