The fact is that you and your method cannot solve even the simplest case (n=2).

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Everything I need to know I learned through Googling.

You wrote a long, information-free prelude, and answered none of my questions. I remind you that you are obligated to answer our questions. I do not consider a long reply to be the equivalent of an answer.

Now that you're back from your suspension, please actually answer these questions. No preludes, allegories or disquisitions, please -- just answers.

I lost interest right there.

Resp Toseek

I must thank you very much for this thing….

And i learned :
In these two days I learned a new technique, how to post equation on to board to some extent. Some equations I could not reproduce exactly. Probably you have to refer to Dynamic universe model paper for some of them. Thanks our friend who suggested this….

http://thornahawk.unitedti.org/equat...tioneditor.php

The Equation 25:
\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}



This is first time I am trying to see equation, it did not show on preview...

Let me tell you some thing in general for the questions in thread……

There are about 5000 different equations for 132 masses in Dynamic Universe model, which can be grouped into about 350 generic varieties. There were about 15 graphs for observing variations of various parameters, changing paths etc. Deriving these equations from the Tensor equations mostly from equation 25 is a long process and took me about 2 years. Because of the testing difficulties for higher number of masses, I tested all these 5000 equations each separately and established correctness separately, initially while I was doing the coding, I don’t know how to test these equation other wise, in totality. [ of course, I corrected many initial problems also. ]

Once I felt this SITA algorithm was working nicely on simulated data, I started inputting the real data from astronomical observations. If the system is correct, I must be able to verify with the real physical data also. That was the final real testing. Once I am thro and the output data was matching with the real observations, I started giving it to you, if some body interested, he can use this algorithm.

This can be developed for other cases like for instance 2 or 3 or 50,000 bodies. Initially, I did not develop it for this type of working. It can be done if needed. For your immediate question to show it for 2 bodies is difficult for me. I feel there is no isolated place in the universe to test the exactness values of movements of two bodies, excluding the other bodies. There is attraction force effect of other bodies is always present. You people are better knowledged and equipped than me, you can show me such places…????.. For example, on sea water which is very near to earth surface, you see the effect of distant moon and Sun. We can not ignore the effects of gravitation of other bodies, near a strong gravitation fields like earth.

That’s why I gave you that equation 1/2 at^2+vt+p can be an approximation for two bodies. I did not say it is exactly that equation, but it works for simple and better understanding for you, nothing else.

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=snp

\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}

Eqn 25 please see the attachment

Attached Thumbnails

 

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=snp

You please tell me what I will get by posting my all replies. Money??? None. No one ever gave me any money except showing hospitality after I go on my own expenses in conferences. Fame ???? None, I got only ill fame. You think only I am making tall claims….. No tall claims . Nothing.

In fact Dynamic Universe model has a large potential and it is showing many other wonderful results. I am presenting only those results that are precisely measurable and are with some better points…..

Because of my mad ness about this Dynamic Universe model, I lost many things in my life. My health is also a problem. In my limited time which is available, I am telling and answering what I can do. In my life I lost all my games due to this mad ness, now there is nothing else to loose….

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=snp

Sir
See the attchment. I have taken care of all these things please go thro derivation.....

==============

[img]http://www.codecogs.com/eq.latex?
Total \,mass \,of\, System = M= \sum_{\alpha=1}^{N}m_{\alpha}\qquad(2)[/Img]
Total force on the particle  is F , Let F is the gravitational force on the  th particle due to th particle.
(3)
F_{\alpha}=\sum_{\alpha=1 ;\alpha\neq\beta}^{N}F_{\alpha\beta}\,-\,m_{\alpha}\bigtriangledown_{\alpha}\phi_{ext}(\a lpha)\qquad(3)
F_{\alpha}=\sum_{\alpha=1 ;\alpha\neq\beta}^{N}F_{\alpha\beta}\,-\,m_{\alpha}\bigtriangledown_{\alpha}\phi_{ext}(\a lpha)\qquad(3)
Moment of inertia tensor
Consider a system of N particles with masses M, at positions X, =1, 2,…N; The moment of inertia tensor is in external back ground field  ext.
(4)

I_{jk}=\sum_{\alpha=1}^{N}m_{\alpha}x_{j}^{\alpha} x_{k}^{\alpha}\qquad(4)
Its second derivative is
(5)
\frac{d^{2}I_{jk}}{dt^{2}}}=\sum_{\alpha=1}^{N}m_{ \alpha}\left( x_{j}^{\alpha}x_{k}^{\alpha}+x_{j}^{\alpha}x_{k}^{ \alpha}+x_{j}^{\alpha}x_{k}^{\alpha} \right)
\frac{d^{2}I_{jk}}{dt^{2}}}=\sum_{\alpha=1}^{N}m_{ \alpha}\left( x_{j}^{\alpha}x_{k}^{\alpha}+x_{j}^{\alpha}x_{k}^{ \alpha}+x_{j}^{\alpha}x_{k}^{\alpha} \right)

Attached Thumbnails

 

__________________
=snp

This is solution for the tensor equation 25. In its solution: I am reproducing this part of my anwer in sted of referring another post....

There are about 5000 different equations for 132 masses in Dynamic Universe model, which can be grouped into about 350 generic varieties. There were about 15 graphs for observing variations of various parameters, changing paths etc. Deriving these equations from the Tensor equations mostly from equation 25 is a long process and took me about 2 years. Because of the testing difficulties for higher number of masses, I tested all these 5000 equations each separately and established correctness separately, initially while I was doing the coding, I don’t know how to test these equation other wise, in totality. [ of course, I corrected many initial problems also. ]

I could not solve the total differential equation, my math knowledge is limited. What I can say is this method also offeres an alternative solution, which you may consider...

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=snp

I tried a tensor solution, insted of trying for N-body Differntuial equations set....

Please check my other posts above.....

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=snp

1. Offers Singularity free solutions

When there are two masses with the same coordinates exactly; SITA simulations give divide by zero error. I mean to say for example centers of Sun and Moon can not coinside with each other. Or any two masses. That means any one mass can have zero zero coordinates. no one another mass sit over there on it.

Other wise I did not find any devide by zero error. Or singularity....

Points 2- 8 were disucces in earlier threads. Any further questions or data are welcome.


Here basically, I want to ask the question ' did any body else Got solution for singularity free N-body solution? ' earlier......... Differential equations or otherwise ......?????

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=snp

1. The above is an example of why you have trouble with your threads. The above is not evidence or proof of anything. It is a claim. People suggest that you avoid answering questions, because this sort of "answer" simply makes more unproven claims.

2. Take a look at post #66, use "edit" mode to see what was done to include your equation. You cannot simply put latex code in your post and expect an equation to appear.

Please also see the FAQ thread: Frequently asked questions

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Please can you show what your system of equations look like for the two body problem, i.e. how the tensor equation (which you don't seem to have defined the terms for) reduces to the two body problem?

This should have been one of the first things that you did when you were devloping your model. After all, if it doesn't work for two bodies, then what hope have you for the general n-body problem?

Thank you sir,

1.You please suggest me where to start in such complex situation. All equations and processes are important and interdependent. I am not avoiding any question. I my self don’t know how to explain. That’s why probably you are feeling like that. How many equations i will explain? Equation 25 is the starting point. You have to use a pencil and eraser to carefully subdivide it into smaller parts.

2. I don’t know so much software. My knowledge in computers is low and simple. I saw what you did, thank you. I will do the same for others.

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=snp

Sir,
Either two bodies or 132 bodies or 50000 bodies, the SITA simulation is same methodology. What difference will it make for you to understand the system if it is 132 bodies? I did not follow your logic. For two bodies, especially, it is dangerous, as it ignores the gravitation force of other bodies in the concept it self as there are no other bodies. Three is not that bad, You have to consider fluctuating gravitational forces. From four on words they will be forming more stable configurations. That’s why I avoided two and three from the beginning. Another thing is that I want to accommodate as many bodies as possible.

Two body problem is untrustworthy to start with, it will lead to confusions, as we can see the presumptions prevailing in the scientific world.

Shall I explain it for 132 bodies?

__________________
=snp

I really would suggest that the application of an original approach to the n-body problem in Newtonian dynamics should, if only for the purposes of exposition (and corroboration), be demonstrated for the 2-body problem.

Of course it may, for all I know, be inherently inapplicable to two bodies, but, if this is the case, then this should be stated and the reason should be given.

So your solution of the general n-body problem cannot deal with the case n=2. Is that what you are really saying?

Then SHOW us how the simple solution to F = dp/dt that I (and others and you) wrote down appears from this miraculous equation 25.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
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“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

snp.gupta Showing a solution for 2 Bodies is important because the mainstream already has a solution for n=2, we can therefore use it to check your solution.

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The logic has been explained to you, and everyone here who has done any science at all understands the rationale. I'll explain it again, so that you cannot claim ignorance (of this particular item): No analytical solution exists for N=132, but ONE DOES EXIST for N=2. So, PRESENT THE SOLUTION YOUR METHOD YIELDS for this KNOWN case. That's part of a verification step. Whether you're a scientist or an engineer doesn't matter -- both cultures rely on verification!

So, for the Nth time, stop your spamming, and just answer the question. If your idea truly has any value, this should be a simple task. Your bizarre resistance to this basic logic strongly suggests that you either have nothing to present, or something to hide.

Just answer the question. It shouldn't take pages and pages of verbiage. Look at a standard physics textbook -- you'll see how compact the solution is there.

There are many practical difficulties. I will have to work out for such case with pencil and eraser for a year again. I gave the approximate equation already. I know this whole exercise will be fruit less. Because it gives practically useless set of equations as there will be no real application.

Reasons I already explained in this thread. If you want me to repeat again I will tell you…

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=snp

Theoretically it is possible for any number of masses. I will have to work it out and tell you the exact solution, which will be time consuming process.....

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=snp

why you want to start it from F= dp/dt ?

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=snp

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

This is not an answer, your "solution" has nothing to do with the problem you are being asked to solve. To remind you, I have asked you :

1. To form the equations that govern the physics of the two-body (n=2) problem.

2. To solve the above equations.

Please do so.

No, it isn't dangerous at all. It is a way to verifying that you can solve the problem with your method.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

I have re-opened this thread at the OP request.

I don't believe that the OP is presenting an analytic solution, but it seems to be a numerical solution. Requests for an analytic solution from the OP would seem to be irrelevant. Anybody?