**2**

# very important equation desentralazing

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#1
Members - Reputation: **364**

Posted 26 March 2012 - 06:31 AM

Then i said, "you can predict how exactly the future will be, you just need to know and relate many f*king things but you can do it"....

"i don't have to calculate the acceleration every frame, that's stupid, the road that every tetrahedron will have across the time just depends on the initial position and velocity when they were created", so i started the process to get the equation of how the acceleration changes through time depending only on its first position and velocities:

http://imageshack.us...captureelx.png/

And there I am, I don't know how to take "a1" to one side alone.

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#4
Crossbones+ - Reputation: **14188**

Posted 26 March 2012 - 07:59 AM

But I am not convinced what you are doing is going to be as fantastic as you think. You will do yourself a favor if you first study a few of the integration methods available (Euler, implicit Euler, verlet, Runge-Kutta...) and learn what their strengths and weaknesses are. Then if you want to explore your own methods, go for it.

You can start here: http://en.wikipedia.org/wiki/Numerical_ordinary_differential_equations

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#5
Members - Reputation: **364**

Posted 26 March 2012 - 08:39 AM

I mean with that new equation i can precalculate collisions and it will be less time spend in calculating collisions collisions, more time spend in having more action, and if i know when something will collide then i wouldn't have that thing were if an object moves at insane speeds it wouldn't collide were it has to.

So now with the control of the fourth dimensions you can get to do very interesting things that are secret for now MUAHAHAHOHOHOHO!!

In some ways i can get to a fifth dimension, can get to a fifth dimension!! and do things with it.

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#6
Members - Reputation: **100**

Posted 26 March 2012 - 12:39 PM

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#9
Crossbones+ - Reputation: **9571**

Posted 26 March 2012 - 11:27 PM

You can certainly plot the trajectories of a group of tetrahedrons for any duration but you will need to do it numerically, and any change in any tetrahedron's position (or adding/removing one), no matter how small, will result in a different trajectory after a given time (because the equations are chaotic). So if you're looking at interactivity there is no difference between precalculating and stepping through each frame.

Unless I misunderstood your problem.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*

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#11
Crossbones+ - Reputation: **3022**

Posted 27 March 2012 - 12:55 AM

Do you just want to solve for a1 in the last equation? If you multiply both sides of the equation by the denominator of the right-hand side and you expand, you'll get a polynomial of degree 3 in a1. That can be solved analytically or numerically."

This equation will only work for two bodies and will not be possible to expand to more, so pretty boring.

People have been working on these problems for hundreds of years, you should listen more carefully on the previous posters. Numerical is the way to go here.

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#12
Members - Reputation: **364**

Posted 27 March 2012 - 01:18 AM

I have a minor mistake in the first equation were i said a1=-a2, it should be a1=-(a2*m2)/m1, I am working with tetrahedrons of same mass so there is no problem there.

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#13
Members - Reputation: **364**

Posted 27 March 2012 - 02:44 AM

http://imageshack.us.../685/sdfjm.png/

i cant do it...can some math expert help me with it. How can I get out of that? there must be someway already invented to solve that cycle of an equation inside the other inside the equation inside the other inside the equation inside the other......infinite.

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#14
Crossbones+ - Reputation: **9571**

Posted 27 March 2012 - 04:31 AM

You don't understand. What you are trying to solve analyticallyhere it is, the equation for whatever number of objects:

http://imageshack.us.../685/sdfjm.png/

i cant do it...can some math expert help me with it. How can I get out of that? there must be someway already invented to solve that cycle of an equation inside the other inside the equation inside the other inside the equation inside the other......infinite.

**has no analytical solution**. I already explained why in my previous post, I will repeat it here - these equations are nonlinear, with feedback (as you noticed with the equation-inside-an-equation pattern). Those types of equations cannot be solved by ordinary algebra. You need numerical methods to work with those.

... unless of course you found an earth-shattering method for doing what everyone has failed to do for many years...

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*

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#15
Members - Reputation: **364**

Posted 27 March 2012 - 04:44 AM

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#16
Crossbones+ - Reputation: **14188**

Posted 27 March 2012 - 04:50 AM

But are you sure, I don't believe that, i have already seen similar problems before,but those are just some weak memories of mine, so the only thing i can tell is that it can be solved,I just need a real math expert to see my equation, i am pretty sure it can be solved. I want Alvaro, the man looks like an expert, Alvaro! come here an tell me...

Here: http://en.wikipedia..../N-body_problem

Now educate yourself and stop wasting everybody's time.

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#17
Members - Reputation: **364**

Posted 27 March 2012 - 01:15 PM

What if i told you i know how to do it, i don't, maybe i will, MUAAHAHAHAHAHAUHUHUHUHU!!!! bye.