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Geek Culture / Math problem - double pendulum rk4

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Rezalt
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Joined: 30th Apr 2009
Location: Denmark
Posted: 18th Dec 2014 10:03
Hello everyone,


Hope math support is allowed in this part of the forum.


I have been working on getting the motions of a double pendulum down by using runge-kutta 4 in excel.

I have gotten these 4 equations:"attached"

Which I should be able to plug in to RK4 method.

I know that the first two equations show the angular velocity, but what do i write in excel?


I have spent way to long at this, and I'm getting tired of feeling like an idot, which surely doesn't speed up the process.


I hope someone out there can help me.


Best regards

- Ollobrains

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Rezalt
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Posted: 18th Dec 2014 11:17
Here is my excel sheet as well.

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Green Gandalf
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Playing: Malevolence:Sword of Ahkranox, Skyrim, Civ6.
Posted: 18th Dec 2014 13:02
The first thing to do is to put all the numbers you know into cells, i.e. things like omega1, omega2, m1, m2, etc. But looking at your image, the first two lines define theta1' and theta2' whereas the rest of the formulae use just theta1 and theta2. Are they meant to be the same thing or are the ones without the dashes just the old values and the ones with the dashes the new ones?

Anyway, once you've clarified that issue, you need to decide whether your angles are measured in degrees or radians - and label your Excel cells accordingly (so you don't forget ). Then, when you use the cos() and sin() functions, just make sure you're using the right units, i.e. degrees or radians. If necessary do the conversion using something like "=cos(radians(theta1))" where theta1 is the cell reference containing the value of theta1. (Incidentally, I'm still using Excel 2003 and the Help file entry for COS() contains a silly typo which might confuse you. I don't know whether that error has been corrected in later versions. You'd think MS would get such things right. )



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Rezalt
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Joined: 30th Apr 2009
Location: Denmark
Posted: 18th Dec 2014 13:18
Hi, thank you for the response


I have uploaded my excel sheet if you want to take a look, but for some reason my messages take a long time to appear on this forum.

I have defined all of the variables that I know, but I am not sure if I know omega, unless we just assume that we are starting with an angular velocity that is 0

The angles in my excel sheet is messured in radians


Thank you for your time ^^
Green Gandalf
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Posted: 18th Dec 2014 17:24
Quote: "but what do i write in excel"


What do you mean? You seem to have written the right sort of thing into your Excel file. However, I haven't checked your cell formulae. I guess that's your responsibility since this sounds like coursework.

Sounds like you need to think about what the various quantities mean.



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Rezalt
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Posted: 18th Dec 2014 18:15
It is actually not part of a course, but I alone have been tasked to try and learn this. We have only really just been through differential equations for a bit this month, making the task a bit harder.

Anyway, I seem to have made a functional double pendulum now. ^^
Atleast the phase plot looks kind of funky.

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Green Gandalf
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Posted: 19th Dec 2014 10:51
Quote: "Anyway, I seem to have made a functional double pendulum now."




Can we have a 3D demo please?



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