Very nice work, from derivation to coding. I don't recall I did the double pendulum at university - but I knew that you only need two degrees of freedom for the mechanics to very quickly get chaotic. Same goes for celestial mechanics.
Hello, I can follow (even perform) the maths to get me to the equations of motion. What I can't follow is the modelling by Python. Is there not some other (easier) method to do this. I am 81 and rather stuck in my ways. Happy New year, by the way.
Really, the only analytical solution for the double pendulum is for special cases - like small angles. If you want to learn the python stuff, I have a series of videos on that - ruclips.net/p/PLWFlMBumSLSaqgYlK2wD7XSPRQ2p-_Tl4
I think dt being 0.0001 yields your code to calculate a lot of data of which only 1/167 gets displayed. Wouldn't it be sufficient to set dt to 1/60 (0.0167) since the screen (your graph) refreshes only at that rate?
the higher your dt is the more accurate the numerical approximation is, dt is actually supposed to be inifinitely small but our computers aren't infinitely powerful so we have to settle for the smallest number we can compute in a reasonable time. if we had a monitor with a refresh rate of 2hz, we wouldn't set dt = 0.5 since the pendulum would imediately start going everywhere and be completely off the actual position it's supposed to be within the frames
@@vilmospalik1480 A reasonable answer and you might be right. Still i would like to see how much the movement would diverge from this if dt was 0.0167. In other words would the errors accumulate or cancel. Interesting.
Very nice work, from derivation to coding. I don't recall I did the double pendulum at university - but I knew that you only need two degrees of freedom for the mechanics to very quickly get chaotic. Same goes for celestial mechanics.
This man really fist pumped the air when he found out his code was right, can't say I haven't done the same
It's just what you are supposed to do. At least, that's the way I was taught.
Thanks for your sharing ! I learned so many things from your video!
Hello, I can follow (even perform) the maths to get me to the equations of motion. What I can't follow is the modelling by Python. Is there not some other (easier) method to do this. I am 81 and rather stuck in my ways. Happy New year, by the way.
Really, the only analytical solution for the double pendulum is for special cases - like small angles.
If you want to learn the python stuff, I have a series of videos on that - ruclips.net/p/PLWFlMBumSLSaqgYlK2wD7XSPRQ2p-_Tl4
There is a simpler way, you can model it using Mathematica NDSolve function, which uses explicit Runge-Kutta methods.
Great video. Thank you
Glad you liked it!
I guess everybody claps along the moment he/she finds out that the mechanical energy is constant so the whole calculations are right!
It’s Hamiltonian is constant of motion
👍
Please upload a video of coding swinging atwood machine in python
oh, that sounds like a fun problem. I'll put it on my list.
I think dt being 0.0001 yields your code to calculate a lot of data of which only 1/167 gets displayed. Wouldn't it be sufficient to set dt to 1/60 (0.0167) since the screen (your graph) refreshes only at that rate?
the higher your dt is the more accurate the numerical approximation is, dt is actually supposed to be inifinitely small but our computers aren't infinitely powerful so we have to settle for the smallest number we can compute in a reasonable time.
if we had a monitor with a refresh rate of 2hz, we wouldn't set dt = 0.5 since the pendulum would imediately start going everywhere and be completely off the actual position it's supposed to be within the frames
@@vilmospalik1480 A reasonable answer and you might be right. Still i would like to see how much the movement would diverge from this if dt was 0.0167. In other words would the errors accumulate or cancel. Interesting.