Uploaded June 2022 | Updated September 2026, 32 minutes ago
In this video, I show you how to handle the double pendulum problem mathematically. We derive the lagrangian, and the equations of motion. We then make the small angle approximation, and calculate the normal frequencies and normal modes.
Typo: In my initial expression for y_1, the angle should be theta_1.
Note: A good point was made in the comments section of this video. What I called an eigenvalue problem isn't exactly that, because neither V-tilde of T-tilde are the identity. One could take the base matrix equation, and multiply it by T-tilde-inverse to convert it into one, but that doesn't change how the system is actually solved. I therefore kept calling it an eigenvalue problem without fully converting it into one.
In this video, I show you how to handle the double pendulum problem mathematically. We derive the lagrangian, and the equations of motion. We then make the small angle approximation, and calculate the normal frequencies and normal modes.
Typo: In my initial expression for y_1, the angle should be theta_1.
Note: A good point was made in the comments section of this video. What I called an eigenvalue problem isn't exactly that, because neither V-tilde of T-tilde are the identity. One could take the base matrix equation, and multiply it by T-tilde-inverse to convert it into one, but that doesn't change how the system is actually solved. I therefore kept calling it an eigenvalue problem without fully converting it into one.
