Equations of Motion for the Double Compound Pendulum (2DOF) Using Lagrange's Equations - Part 2 of 2
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- Опубликовано: 3 окт 2024
- Download notes for THIS video HERE: bit.ly/37QtX0c
Download notes for my other videos: bit.ly/37OH9lX
Deriving expressions for the kinetic and potential energies of a compound double pendulum using a systematic approach for use in the method of Lagrange's equations. Two degree of freedom system.
Very informative. Thank you for your videos!
Very helpful. Thank you!
Thank you very much, great explanation. Could you please do a video doing a linearization for these types of problems or could you point out to another video doing the linearization? It would be extremely helpful as well.
Yep. Thanks for the suggestion. This is definitely a video I will make, but I have a few to make ahead of that.
Your videos are so helpful thank you
Hello Sir! I have a question: Why in the video of the inverted pendulum there is no rotatory kinetic energy associated using 1/2 * J * Theta_dot^2? Thank you.
In the inverted pendulum problem, the mass was treated as a point mass - so it has no rotatory inertia. I probably should have been more clear about this. The reality is that for a simple pendulum, typically the rotational kinetic energy is insignificant when compared with the translational kinetic energy UNLESS the diameter of the mass is very large.
Great vid, i've never seen lagrange eq's in any other form than "=0", could you point anywhere out where i can learn about the "Qi" term you include?
The Q's are generalized forces and the are incorporated into the into Lagrange's Equations using the Principal of Virtual Work and a method known as the Extended Hamilton's Principal. Here a reference that explains it: web.mst.edu/~stutts/SupplementalNotes/Lagrange.pdf but there are many others online. Just search for "Lagrange's Equations Generalized Forces".
Hello, Lagrange analysis is fairly new to me. I see sometimes that the Lagrange equation is equal to zero sometimes it is not - there is a multiplier (lambda). Please can explain briefly why it is necessary in some cases and not in others?
According to LaGrange's method, any moment applied at the hinge would appear on the right hand side of the corresponding equation. So a moment at hinge 1 would appear on the right of the first equation and similarly for hinge 2 and equation 2. In this problem we do not have any externally applied forces or moments, so the right hand side of each equation is zero.
The Lagrange multiplier, λ, is something different. This is used when adding constraints to the system (which doesn't occur here).
For J1 why is there an additional m2*l1^2?
This is just something which comes out of the math as I have treated it. Physically, it describes the fact that as the angle θ1 changes, we also need to consider the fact that m2 is providing a resistance to this.
If you had concentrated masses on the two links would there still be moments of inertia?
Yes. These masses will still have a moment of inertia about their rotation point. However, if they are point masses, then they will not have a moment of inertia about their own c.g. These masses would add to the moment of inertia for each bar.
Do you have any reference material or books where I can learn more about how to add none conservative forces and external forces for say control purposes.
I don't have any books on Controls to recommend, However, I would recommend the RUclips channel of Steve Brunton (ruclips.net/video/qjhAAQexzLg/видео.html) if you'd like to learn how to combine a structural model with control theory.
@@Freeball99 Sry forgot to respond when I initially read the comment (was drunk at a party, probably for the better), I have used the euler lagrange theory to develop a state space representation of a two wheeled self balancing robot, and Stevens great videos in part to help develop the controller. But when it comes to euler lagrange i would have struggled to incorporate say a force acting on the secound body only in one of the global directions. I can't think of any real systems where such a force would exist. I have started reading trough the notes you linked to in your response to chamelious and there are some pointers in there :)
5:12 did you forget to include J1 and J2 at equation 8 ?
No. On the line before, I incorporated these into the definitions of Ja and Jb.
very useful thank you very much
Pog dude