Equations of motion for a double pendulum
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- Опубликовано: 25 авг 2024
- Here is my derivation of the differential equations of motion for a double pendulum using Lagrangian mechanics.
Here is my introduction to Lagrangian mechanics
• Introduction to Lagran...
If you want to look at all the equations, I also wrote this up on my medium site:
/ finding-the-equation-o...
PART II
Here is the video for part II in which I model this double pendulum in python
• Modeling a Double Pend...
Hello! I'm a studying Physics in Germany and I have learned a lot through your videos. Keep up the good work!! Thank you so much for this cool explaination:)
thanks! Glad you found them useful!
Am a high school student. Found the video easy to follow, while writing the equations myself. Really like this video.
I will be honest. When I was in high school, I wouldn't understand any of this. Good job keeping up.
Thank you so much for posting this version of your walkthrough. It is so important to see how someone who knows what they are doing thinks through not only what they do right, but what they mess up on. I teach high school physics and it is a rough first month because I need to teach students how to think through difficult/complicated problems instead of rage quitting. Thank you thank you for modeling solid problem solving and critical thinking!
I haven't watched it all yet, but at 17 minutes in this is fascinating!
Nice explination , Nice use of the Lagrangian.
Excellent walkthrough. Thanks!
Great video. Thank you
30:37 I hope you notice it but the other term should have the d/dt(θ_1 - θ_2)
nevermind, you did @31:22
Even though I caught it, thanks for watching my back.
Good explanation! One thing you could perhaps improve upon is to more clearly label the axes you chose.
Thanks for the good explanation, I want to ask why the double pendulum has the equation of centripetal acceleration(has theta1^2)? not like the single pendulum case?
That shows up because we are using polar coordinates (it comes in indirectly since this is using the Lagrangian).
Hello! Just woukd like to ask, in T2 why did you put a 2 in front?
21:53
could you please explain this equation in more detail? I'm currently in high school and I'm having a hard time trying to understand it.
If you don't understand that equation you should first consider taking a differential equations course, but to answer your question it is the derivative of the Lagrangian respect to the first derivative of the generalized coordinate (in this case theta), then you derive the result respect to the time and finally you subtract the derivative of the Lagrangian respect to the generalized coordinate, that you equal to zero due to the fact that there aren't non-conservative forces actuating in the system.
hello, why can we not use taylor series to approximate cos theta and sin theta
yes, but that still limits you to a small angle approximation.
Is it just me or is there no sound?
why can't you solve the differential equation analytically?
I'm not sure if there is an exact analytical solution to this equation - the best bet is to look at special cases (like normal modes and small oscillations)
that's one question i personally don't want to answer, because wallahi that seems like a very hard question to answer.
I thought it was not even possible for single pendulum equation, since it depends on its initial angle and angular velocity. However, it is possible when you constrain the angular velocity.. so there are many videos finding an equation for θ when ω = 0.
I could be wrong though correct me please if I'm wrong or confirm if true