German teen Shouryya Ray solves 300-year-old mathematical riddle posed by Newton

[blixel]

I saw this article on slashdot and thought it was interesting, and very relevant to Orbiter. I searched the forum and didn't see any mention of it, so I thought I'd post it.

My thought was, if this has never been completely understood before, then all current simulations must be currently flawed to some extent. Perhaps the new math will allow for truer-to-reality realism?

 

[Calsir]

My thought was, if this has never been completely understood before, then all current simulations must be currently flawed to some extent. Perhaps the new math will allow for truer-to-reality realism?

The problem was never solved analytically. It does not mean that it was not understood.

 

[RGClark]

I saw this article on slashdot and thought it was interesting, and very relevant to Orbiter. I searched the forum and didn't see any mention of it, so I thought I'd post it.

My thought was, if this has never been completely understood before, then all current simulations must be currently flawed to some extent. Perhaps the new math will allow for truer-to-reality realism?

That is very interesting news. I didn't know it could be solved exactly. The numerical approximations can be quite accurate though.


Bob Clark

 

[Marvin42]

Does anyone know what the problem was (the equations)? And what was his solution? Some press say there were two problems solved but it seems it all started from a Daily Mail article (which is a tabloid, you know). If you know, please share with [ame="http://en.wikipedia.org/wiki/Talk:Shouryya_Ray"]Wikipedia:Shouryya_Ray[/ame] and here also.

Sorry Daily Mail just copied, found the source of the media news: http://www.welt.de/print/die_welt/vermischtes/article106355324/Zahlen-bitte.html

 

[jedidia]

Does anyone know what the problem was (the equations)?

If there would already have been equations, the problem would already have been solved

Analytical solving of a problem is not a basis to understanding it. It is "merely" the kings road to getting an accurate result. If you don't have an analytical solution to a problem, it means that you don't have an equation where you put in all the values at one end and get the results at the other. Istead you have to solve the problem incrementally (in physics, this usually means breaking it down into small time steps, which is how orbiter "solves" the n-Body problem. That means that the more accurate you want it, the more iterations you have to run. An analytical solution provides you with an equation that gives a correct result without breaking the calculation down into several iterations, and therewith can save you considerable computing power (or a lot of time if you happen to run it on paper) while providing a more accurate result.

Now, if that boy genius could also solve the n-body problem, we could make somewhat more accurate MFDs...

And what was his solution?

Nothing I can make even the slightest sense out of...

 

[RGClark]

Does anyone know what the problem was (the equations)? And what was his solution? Some press say there were two problems solved but it seems it all started from a Daily Mail article (which is a tabloid, you know). If you know, please share with Wikipedia:Shouryya_Ray and here also.

Sorry Daily Mail just copied, found the source of the media news: http://www.welt.de/print/die_welt/vermischtes/article106355324/Zahlen-bitte.html

This forum shows the equation:

Teen Solves Newton’s 300-Year-Old Riddle - An Indian-born teenager who lives in Germany has solved a mathematical problem posed by Sir Isaac Newton that's baffled mathematicians ever since.
http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4sxd91

It appears it is assuming the air density is constant since the air drag depends only on the velocity, not altitude. So this must be for a projectile close to the ground.

Bob Clark

 

[Notebook]

Daily Mail is a rare source of mathematical truth, or any other kind.

N.

 

[RisingFury]

The only part I have a problem with is the beginning... did he just pull that function out of his...?

I hope he found a way to arrive to the solution and didn't just guess by adding and removing terms.

 

[Goth]

Pretty interesting:
[ame="http://en.wikipedia.org/wiki/List_of_unsolved_problems"]List of unsolved problems - Wikipedia, the free encyclopedia[/ame]
I would like to pick up one and spend days trying to solve one, since I like staying at home doing nerdish stuff but... I should first know those sciences. LOL

I hope he found a way to arrive to the solution and didn't just guess by adding and removing terms.

From here:
http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4t03fl

I just don't understand how this was never done before. What's so astonishing about it?
Answer:
A few mathematical tricks in order to achieve separation of variables. The brilliant part is that uv'-vu' becomes u2 s' which lets you divide u over. Once you have the idea, the deriviations are remarkably easy. The hard part is envisioning an equivalent form of the equation where the solution is apparent. I would probably have given up after staring at the third last equation for a few hours.

Don't know anything about what I'm posting, just trying to give you the sources.

 

[wledzian]

The first formula in that article boils down to a re-arrangement of:
F = mA
--> A = F/m
with velocity and acceleration written in vector form.
Knowing Drag = 0.5*(density)*Cd*(velocity)^2, we can assume that his friction constant:
C = 0.5*(density)*Cd / (mass).

It's been too many years since I've had to solve a differential equation by hand to reproduce the results without consulting my textbooks, but this exact problem and the full analytical solution was the first example given when I studied DiffEQ towards my BSAE. Most definitely not unsolved.

This same problem, when altitude-based density and gravity are incorporated, becomes much more challenging. Replace cartesian X,Y coordinates with polar coordinates planar with the trajectory around a spherical body, and x'^2 + y'^2 is no longer equal to v^2. Add also the reality that while it can generally be said that
Drag = 0.5*(density)*Cd*(velocity)^2
and Cd tends to be constant for a wide range at moderate Reynold's numbers, it varies greatly at low Rn and approaching/exceeding the local speed of sound.

Finally, it is of great importance to note that the real atmosphere , unlike the 'standard atmosphere', is not a fixed, known quantity.

For all these reasons and I'm sure some that I've forgotten, numerical solutions with lookup tables are typically far more useful in reality than purely analytical solutions.

I suspect there may have been more to the original problem than what's listed in the Reddit link. That a 16-year-old high school student figured it out on his own 'out of curiosity' is none the less very impressive.

 

[ex-orbinaut]

Sorry for the necropost, but I found this thread extremely interesting. Thanks for posting.

Funny old thing. Some time ago last year I rekindled an idle interest (and my interest in anything is, truthfully, never really more than idle) in understanding the phenomenal performance of the 20.3 cm guns mounted on the German cruisers of the WWII Hipper class. I cobbled this ballistic trajectory simulator together, extrapolating on some aerodynamic and momentum formulae that were gathering mental dust in my turbid head. Then I had some fun throwing around shells of different diameters, velocities and weights, for a while. The results were quite accurate. Someone here might find it transiently entertaining, too.

I used lookup tables and interpolation, initially, and was playing around with the idea of attempting to model Cd variations at different velocities, when I lost interest (actually, vacation ran out).

It would be nice to know what models for that purpose currently exist...