I hope you you are not testing my class 10 high school knoledge. I passed it out.
What is actually in your mind , please spell out....

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=snp

Thank you sir,

This I will try

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=snp

No, I am asking you to solve the problem for the case n=2. Please answer the question.

No , In his post he was asking me symbolic solution, thats why i referred to Equation 25 math section of paper.

For calculation of numerical solution in Dynamic Universe Model, you have to give me initial values of 133 masses. I.e. you will have to supply their initial three dimensional ‘positions, velocities, accelerations’ and actual values of masses. Then the numerical values can be calculated. I did it that way.

This calculations program can be setup 2 , 3 or 50000 as required, But it will take time for setting up and testing. It may be few months. You please give me other values

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=snp

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Brett
Peters Creek, Alaska
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Sir,
I need some rest and sleep in between, I am answering, your questions….

I am asking the unknown things about how to present equations on to this board. This is an examination for me. How can be the questions known to me? I will have to answer them spontaneously by seeing the questions.

Yes you are correct mainstream says it is not possible to solve N-body problem without a singularity. I am giving this possible solution I worked out and tested for 17 years.

Don’t worry sir, I am trying my level best, to explain my situation and solution as my limited English permits.….

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=snp

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

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=snp

Yes sir,

i asked a clarification only. what actually in his mind.

This model can be applied for any number of masses. But i worked it out for 133 masses. I need time to set it for other number of masses. It can be done. I gave the equation of motion for 2 bodies. the model will become so....

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=snp

No, it is not. Please form the differential equation that describes the motion and you will find out that your simple-minded solution is incorrect.

Now for the case of three body part of your question,

The model simplifies to same equation of motion for each body.

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

These particles collapse into each other, as they are in single line in your case.

And when they are not in single line, the above equation will change into three dimensional vector form, the resultant direction vector will change from time to time..,

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=snp

No differential equation is formed here in Dynamic Universe Model. Only simple and tested engineering equations are used. I did not get your point, may be if this answer is not sufficient, please clarify…..

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=snp

For the second time, you got the wrong solution, this is more complicated than what you learned in 9-th grade kinematics.

For the second time, form the differential equation that describes the motion and try solving it. Correctly.

That's too bad because mechanics is based on solving differential equations.
Are you telling us that you don't know how to form the differential equations that describe the motion? If this is the case, how can you pretend that you solved the n-body problem?


The point is that you need to be able to form the differential equations that describe the motion. Do you know how to do this?
After you formed the differential equations that describe the motion, you need to solve them. Do you know how to do this?

You must understand that offering an alleged solution for N=133 raises many questions. An ungenerous skeptic might suspect that offering a solution for such a large number of bodies is motivated by the knowledge that no analytical solution is available to falsify it. That is why it is important to test your "solution" for the couple values of N for which analytical solutions are already available. If your method does not yield the known solution for N=2, then we know there's a problem. Indeed, you should have done this validation yourself in debugging your code. It seems from your inability to produce this reference solution that you have not performed this essential first check. So here's one direct question:

Q1: What checks, if any, did you perform to validate your code?

You also say that no differential equation is involved. Then that triggers the following question:

Q2: What "simple and tested" equations did you use in your simulator?

Finally,

Q3: Since these are "simple and tested" equations, it should be correspondingly simple to generate the solution for N=2 and perform the comparison. Would you now do so?

Cool thanks slang,

I like this toy.
better then my
(V₁+V₂)/√(1+(V₁V₂/C²))

These are all outcomes after solving equation 25, which I referred in Dynamic universe model. In simplified language i explained you these for case of 2 bodies and three bodies.

This is different direction, many people tried in that differential equations direction. But there is no outcome. These are some of the changes made in Dynamic Universe model. if you feel diff eqn is the proper direction , you can try your self. i can explain what is done here, what good it achieved
.

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=snp

Well, then they are the wrong outcomes because you don't know how to write the correct equation.
Let me try to help you: start with F=GMm/r^2. Now, add to this F=dp/dt where p is the linear momentum.

Q4: Can you write the correct equation now?


Really? I thought that all self-respecting physicists who know what they are doing use differential equations. You didn't know about this?


Q5: Then explain what equation generates your wrong solution 1/2at^2+vt+p?

So, stop dodging and please answer the questions Q1-5. Under the BAUT rules you are expected to do this.

This approach is slightly different from forming differential equations and solving. We can not get solutions in that direction. People tried . You already know that. That’s why there was no singularity free solution earlier. Can you please tell me who got solution in that direction….?

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=snp

Please stop dodging and answer the questions.


Certainly not you. The naive 1/2at^2+vt+p applies only in 9-th grade, not in serious physics and certainly NOT when the force is GMm/r^2.

Q6: So, you don't know how to derive the solution, right?

Q7: If you can't solve the simplest case (n=2) I gave you, how can you expect any of us to be convinced that you can solve the general case?

But for the case of N=2, your approach should yield the same solution as the differential-equation based solution, right? This goes to the question that I have asked that remains unanswered.

I would also like to point out that I just checked several online engineering textbooks. They seem to be full of differential equations, so I am mystified about the meaning of your phrase "simple and tested engineering..." equations.

Yeah, but after years on the internet, I can read the bottom one with no problem.

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The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

You should not have to supply any values for the accelerations. The should come from the masses of the bodies and the force law of Newtonian gravity.

Are you really inputting the accelerations by hand?

No never, But possibity and provision exists....
Regards
=snp

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=snp

Welcome. One technical issue is that when that website fails or stops, all your equations disappear from your BAUT posts... so it's probably smart to use it sparingly, include the LaTeX code at the bottom of your post, and/or to save the resulting image to your harddrive, and upload it to BAUT as an attached image (which also has its drawbacks for unregistered readers :/ ), and/or also include the written version of the formula.

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Meet the OOONG TOE.

Apparently you don't understand that your equation:
0.5 a t² + v t + x₀
IS a solution to a differential equation.
But then, you don't do the math, do you, you have it done for you by someone else.

This whole thread is going to be EXACTLY the same nonsense as before, isn't it?

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Then stop dodging and answer the precise questions you have been asked. You are doing the same dance as in the previous threads.

The LaTeX code is embedded in the URL, and there's other services providing similar functionality. If "http://www.codecogs.com/eq.latex?\frac{V_{1}+V_{2}}{\sqrt[]{1+\frac{V_{1}V_{2}}{c^{2}}}}" fails, you can edit the URL to use one of these services:
http://www.forkosh.dreamhost.com/sou...tml#webservice

Some sites make this or similar services available to their users...it can be set up to check the referral header to restrict usage to posts on the forums. Maybe something to consider here...

Dear sir,

I am not dodging any questions,

some questions need some serious thinking. and fresh mind, i need some time to think.

Some simple questions I am answering first.....

If you feel, that should not be done, I will have to stay in the same order, in which they were asked, then I will stay in that order.

I hope this is what you meant by dodging.

From now onwards I will stay in the same order they were asked, probably that will solve the problem of dodging? If not please explain me what is meant by dodging???

Regarding, equation 25, I am still not able to reproduce on forum page, I am helpless in this regard, that’s why I am referring it like that. My computer knowledge is limited….
I will make more trails….

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=snp

Instead of going straight into answering your direct question, I also will put a prelude first. I will answer all your questions one by one.

Those days say about almost 17 years back, after writing those equations given in the mathematical background of Dynamic universe model, I started the lengthy process of solving those equations in the usual differential equations method. Soon I stopped on some day, as I was not reaching any end. I believe in Goddess Vak, She gave me this approach next day early morning. Later I worked out that solution for a year or two. I felt it is a promising approach. It is a numerical calculations approach. That time internet was not freely available in India. I was to search books and magazines, what ever possible with in my limited purse. That time I did not know what other researchers were doing exactly for N-body problem. I know they do with some expensive super computers. I don’t have expensive computers. Of course I don’t have them even today. I don’t know weather such prelude can be written in BAUT forum. If it is to be deleted, I will delete, please let me know about it, I will do that in my next edit.

Now coming to the points you indicated, testing of the solutions and of course visualizing the large output data which is very simplified now a days, and was very difficult those days.

A. There are many reasons for ‘why132 masses?’ question. This question has both the sides. For higher number of masses as well as lower side. Now for the higher side…

1. When this Dynamic Universe Model project was started in the beginning of 1990’s, the availability of computers to a common man in India was very scarce. It was that period, where processor is 8088. The PC with two floppy drives were endangered species and hard drives are entering the field. There were limitations of capacity of data handling.


2. Computers in those days used to take few hours to calculate something like 50 iterations, which drastically reduced to 8 to 10 min today with a five year old laptop.


3. Milkyway, our Galaxy has estimated 10^11 Stars approximately. Number of planets will be additional 10^12. We can estimate number of dwarf planets to be 1000 times the planets, say about 10^15. What about chunks of planets and asteroids? They may be a million times the number of planets, say about 10^18. All these figures were taken on the lover side for an approximation. Hence about10^19 masses and their position data are required for simulating a Galaxy. Now there are millions or trillions of Galaxies in the Universe. What will be the total number of masses required to simulate? It will be about 10^25 to10^28. Is there any Super computer on Earth which can handle such huge amount of data, today? Do we have all such data to feed the computer?


4. May be 132 masses, are less for a simulation. But even 3 body problem is not simple to solve. Even if we make a simulation with million or 10 million masses it will be on the order of 1020 times less than that is required for simulating the universe. We should be practical in our thinking. I don’t have access to higher computers. I am a poor man. I don’t have resources.

B. Coming for the lower side……….

Those days I did not think for the lower side at all. What I was aiming is to go for the highest. I did not took it in the way of mathematical induction process, that if it is true for n=2, and n=3, test for n and n+1. I got no way of testing that approach. I don’t have differential higher value to test my solution probably some of you can explain me how………………

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=snp