In the phase diagram picture, what are those lines above and below the closed loops, is it suggest that if the pendulum moves to fast the ball will break off and fly of to infinity?
Daniel, good question. The lines above and below correspond to the case where the pendulum keeps turning in one direction, over and over, like a windmill. There's no going off to infinity since the angle variable is cyclic. More at 5:52
Thanks for that. That was helpful to see the pendulum moving as the dot on the phase space traced through the orbit.
Thank you. I love to be able to provide helpful visualizations whenever possible.
These are really great lectures on nonlinear analysis.
Thank you ❤ From Nepal
Awesome explanation professor.
Glad you liked it
Thanks for the lecture
So nice of you
Very cool stuff great insights!
In the phase diagram picture, what are those lines above and below the closed loops, is it suggest that if the pendulum moves to fast the ball will break off and fly of to infinity?
Daniel, good question. The lines above and below correspond to the case where the pendulum keeps turning in one direction, over and over, like a windmill. There's no going off to infinity since the angle variable is cyclic. More at 5:52
jefe