Number, Symbol, and Plot

[ValeryOchkov]

The site of the article "Решение задачи на компьютере: число, график, символ"

The numeric solution

The symbolic solution

[AlanStevens]

The numeric version seems to work ok (i.e. without the sudden flips) if formulated as in the attached.  It works because x3 is always greater than x1 and y3 is always less than y2.

Alan

[ValeryOchkov]

OK!

And what about the trace of the point 3?

And more! I do not know how to translate it into English:

Нет ничего практичней хорошей теории!

Нет ничего численней символьного решения задачи!

[AlanStevens]

I assumed you were only interested in getting point 3 to travel smoothly without the sudden large leaps. I’m unable to look at the trace aspect at present- I’ll take a look later.

Alan

PS I don’t know how to translate the Russian either!

[ValeryOchkov]

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@AlanStevens wrote:

PS I don’t know how to translate the Russian either!

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May be so

There is nothing so practical as a good theory.!
There is nothing so numerical as a god symbolical solution of a problem!

[Werner_E]

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@ValeryOchkov wrote:

OK!

And what about the trace of the point 3?

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You would turn the solve block into a function of beta and precalculate it. As its independent from FRAME it won't calculate again for each Frame.

Attached is a way to do it based in Alans worksheet.

If like it the way your animations shows you could also let the mechanisma "draw" the trace by including the trace in the animation and plotting just part of if depending on the value of FRAME.

I don't like it to show the trace with evenly spaced dots or line segments as in your animation but would rather prefer that the speed at various positions can be seen in the trace, too as in the one I provided above. Maybe just a matter f personal taste, though.

BTW, I agree that its nice to have a symbolical solution to a problem but for many (most?) real life problems we must be happy if we have at least a numerical solution.

[Werner_E]

This is what I was talking about:

Necessary changes:

[ValeryOchkov]

It is fine!

But I think about vectors of velocity too!

[Werner_E]

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@ValeryOchkov wrote:

It is fine!

But I think about vectors of velocity too!

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Sure, why not!

[ValeryOchkov]

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@Werner_E wrote:

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@ValeryOchkov wrote:

It is fine!

But I think about vectors of velocity too!

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Sure, why not!

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Theoretical mechanics consists of three sections - statics, kinematics and dynamics. Speed should be considered only in the dynamics! See please three my planets above! But Werner solutions is fine! I will try to us it for one dynamic problem!

For same for example