Nice video, an interesting example of Hamiltonian system for us beginners. Just one minor suggestion, it would be better if the sound of the pen scratching the glass can be eliminated.
Greetings, great video I have one question, how do you know then the direction of the center and saddle, also this result is constant? meaning that every minimum in the hessian will be a center and every max a saddle? Thank you for your great work!
For a Hamiltonian system (in 2 dimensions), the solution trajectories lie on the level sets of the Hamiltonian function. When you compute the Hessian of the Hamiltonian and find the eigenvalues, you will see that local maxima or local minima become orbits (or centers) and saddles remain saddles.
Nice video, an interesting example of Hamiltonian system for us beginners. Just one minor suggestion, it would be better if the sound of the pen scratching the glass can be eliminated.
Thanks for the view! In newer videos I am working on filtering the noise out.
Greetings, great video I have one question, how do you know then the direction of the center and saddle, also this result is constant? meaning that every minimum in the hessian will be a center and every max a saddle?
Thank you for your great work!
For a Hamiltonian system (in 2 dimensions), the solution trajectories lie on the level sets of the Hamiltonian function. When you compute the Hessian of the Hamiltonian and find the eigenvalues, you will see that local maxima or local minima become orbits (or centers) and saddles remain saddles.