Uploaded May 2018 | Updated September 2026, 2 weeks ago
After a long hiatus from this Nonlinear Dynamics, I have finally returned with a 4th video! In this lesson, I begin with proving that oscillations for a 1-D autonomous dynamical system of the form dx/dt = f(x) are IMPOSSIBLE.
Then, I introduce the concept of potentials of differential equations. Potentials are another useful way of examining a differential equation and are convenient quantities because they behave in a manner similar to potential energies in Physics (i.e. physical systems prefer a state of lower potential energy, similar to how dynamical systems here tend to lower their potential over time).
After introducing potentials, I finish off by solving a quick example problem which shows how potentials can be utilized to ascertain the behaviour of a nonlinear ODE.
Questions/comments? Let me know below!
Pre-reqs: The videos before this one on this playlist: youtube.com/playlist?list=PLdgVBOaXkb9C8iPDD5xW0jT-c3dtP4TR5
Lecture Notes: drive.google.com/open?id=1Uyr2UB5hugKQaBi7JAlyFYvGj_KIww2O
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- James Mark Wilson
- Marcin Maciejewski
- Sabre
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
- Bernardo Marques
After a long hiatus from this Nonlinear Dynamics, I have finally returned with a 4th video! In this lesson, I begin with proving that oscillations for a 1-D autonomous dynamical system of the form dx/dt = f(x) are IMPOSSIBLE.
Then, I introduce the concept of potentials of differential equations. Potentials are another useful way of examining a differential equation and are convenient quantities because they behave in a manner similar to potential energies in Physics (i.e. physical systems prefer a state of lower potential energy, similar to how dynamical systems here tend to lower their potential over time).
After introducing potentials, I finish off by solving a quick example problem which shows how potentials can be utilized to ascertain the behaviour of a nonlinear ODE.
Questions/comments? Let me know below!
Pre-reqs: The videos before this one on this playlist: youtube.com/playlist?list=PLdgVBOaXkb9C8iPDD5xW0jT-c3dtP4TR5
Lecture Notes: drive.google.com/open?id=1Uyr2UB5hugKQaBi7JAlyFYvGj_KIww2O
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- James Mark Wilson
- Marcin Maciejewski
- Sabre
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
- Bernardo Marques
