Animating the Double Pendulum (2DOF) - Part 1 of 3 - Solving the Equations of Motion

[@calebhyde2783]

Hi, thanks for these amazing tutorials. Seeing the full derivation through to a Python and pygame implementation is great. I've been following along today. When you convert the eqn's of motion to matrix form (starting at 1:28), I believe you left out the exponent on theta_2_dot on the right hand side (f1). You have it squared in the number eqn 1 above, and then when you get to the code, you have it right again, with "a2d*a2d" in the full line: f1 = -m2*l2*a2d*a2d*sin(a1-a2) - (m1+m2)*g*sin(a1). Thanks!

[@Freeball99]

Yes, you're correct. The first equation, right-hand side I'm missing a squared on the θ2_dot. Thanks for catching this. The rest is correct.

[@exanjohndelafuente.carpio3738]

Good Morning Sir where did you get the two equations presented in 0:26?

[@Freeball99]

This was from a previous video. The link to it is in the video description.

[@DD-zv3yc]

Hi, I have a proble with your solution, because of the way you put the reference system, If I put theta1 and theta2 equal to pi / 2 and the two angular velocities equal to zero, then the energy will be equal to zero, and it is assumed that the system would not have to oscillate

[@draganostojic6297]

Great, keep a great work!

[@eduardodossantos3099]

Great keep going

[@choguerrero]

Hi Andy! Thank you so much for these videos! they are very useful indeed. I what to ask a very simple shallow question, how to change the setting of text appearance? I like so much the contrast you use in your scripts. I am using Spyder, I managed to change so far some of the colours of part of the next, but I have not found how to change the colour of the equal sign "=", and the second keywords in the commands i.e. array or append in np.array, Y.append. Thanks!

[@Freeball99]

I believe you are referring to the syntax highlighting for Python. This is a feature of the text editor that I am using (Sublime Text). I believe this is the default theme although it does allow one to use various different themes which can be installed. Most text editors should offer varieties of this.

[@obasho856]

Hi, can you share wich ide you are coding on?

[@Andy-hy8px]

I'm using Sublime Text. It's just a text editor and not an IDE.

[@obasho856]

@@Andy-hy8px for animation?

[@Andy-hy8px]

@@obasho856 I am using the Pygame library for animation and running the code within Terminal on my Mac.

[@obasho856]

@@Andy-hy8px okk sir, thank you

[@engdoretto]

Awesome!

[@dylaninho2500]

Hey there, when you used f =ma at the beginning, how did you know that the right part of the equation was a force? Also do you recommend any resources to learn the method used such as state space form? Thank you!

[@Freeball99]

This is because the equations of motion represent a balance of forces. Even though in this case we derived the equations of motion using the Lagrangian approach instead of Newton’s Law, the resulting equations are really a force balance, F=ma, where ma can be considered to be the inertial load - which is a force. The truth is that, in this case, the right hand side are not really forces, they are moments and, in fact, the equations were then divided by mass and length, but they were derived as forces. But for the purpose of solving the equation, it’s fine to assume the structure that I have. With regards to state-space form, I have other videos where I explained this more thoroughly. Take a look at: kzbin.info/www/bejne/m2LUZal6Z7Cdpqc

[@dylaninho2500]

@@Freeball99 Thank you, Thank you, On the graph I have generated, the angle of theta2 is going above 8 which is too large, do you know why this is?

[@abdullahcakan]

Hi, excellent videos.. What software do you use while writting to screen ? Do you use a graphical tablet?

[@Freeball99]

I’m using an iPad Pro 13-inch with Apple Pencil. The app is called “Paper” by WeTransfer.

[@Vxt943]

Great