The Hamiltonian might seem the last choice, but it is actually very powerfull. Computers like the Hamiltonian formulation because it goes well with numerical integration.
Can you PLEASE do more problems with hamiltonian? Some examples for classical and/or using it in quantum? You have a lot on the lagrangian but, bot hamiltonian!
Finally Hamiltonians!! Thank you so much Just a question, how do you include external forces that arent conservatives? In Lagrangian and Hamiltonian :(?
Because this is only Classical Mechanics; later in Quantum Mechanics the Hamiltonian will be very useful, so it's nice to see how it sits in simple Classical Mechanics compared to the Lagrangian. Also, the Newtonian approach is basically a derivative of the others and therefore contains less universal truth; for example, Newtonian Physics is not invariant under reference frame transformations; drastically speaking, Newtonian Physics are wrong, because the laws of Physics cannot be different in different reference frames. Or put another way, Newtonian approaches do not survive a Lorentz transformation (or demand that the speed of causality is infinite instead of c). But the Hamiltonian goes all the way through and is still around in Quantum Mechanics later as an operator acting on the quantum states, as essentially "energy", as we can already see in its roots here as the sum of energies in classical mechanics.
I personally can’t say for Hamiltonian Mechanics but I have worked with Lagrangian Mechanics and it does really help in cases of spring systems. For example if there are multiple masses on springs with dampers, using Newtonian Mechanics might not be the most fun experience but using Lagrangian Mechanics can simplify deriving the differential equation.
your channel is a gem. thanks for doing the H and L side by side.
Thank you. Glad you found our videos. 🙂
The Hamiltonian might seem the last choice, but it is actually very powerfull. Computers like the Hamiltonian formulation because it goes well with numerical integration.
The Hamiltonian technique is indeed a powerful technique.
Thank You Sir Michel
Can you PLEASE do more problems with hamiltonian? Some examples for classical and/or using it in quantum? You have a lot on the lagrangian but, bot hamiltonian!
It is on our list of things to do, but we are currently working on some other topics.
@@MichelvanBiezen I’m going to be real my guy I think I have commented this years ago and got a similar response.. it’s been 8 years man.
@@MichelvanBiezen seriously though I appreciate the insane amount of content you have provided us. I am forever in your debt!
Thank you!
Profesor can we say that langrarian takes the whole system in parts and the Hamiltonian takes the whole system as one part?
Can you suggest a book with Hamiltonian mechanics practice
Unfortunately, I have not yet found a good book with good examples.☹
Finally Hamiltonians!!
Thank you so much
Just a question, how do you include external forces that arent conservatives? In Lagrangian and Hamiltonian :(?
That will introduce a damping factor, so it depends on what type forces we include. We'll have to make some videos on that as well.
Fantastic video
Thanks! 😃
@@MichelvanBiezen very good Dr , can you let me same advice to helping my in my exam ? please 😕
"Wonderful Explanation Sir 😄😄😄😄😄😄😄."
Thank you so much 😀
👍
Hmm. If both methods: Lagrange's and Hamilton's ones come to Newton's equation, why to bother? :)
Some systems are extremely complicated to solve using Newtonian mechanics, which is why we turn to Lagrangian/Hamiltonian Mechanics
@@darkbullet78 I'd like to finally see an exemple . Because most of lectures focus on killing an ant with the nuclear weapon...
Because this is only Classical Mechanics; later in Quantum Mechanics the Hamiltonian will be very useful, so it's nice to see how it sits in simple Classical Mechanics compared to the Lagrangian. Also, the Newtonian approach is basically a derivative of the others and therefore contains less universal truth; for example, Newtonian Physics is not invariant under reference frame transformations; drastically speaking, Newtonian Physics are wrong, because the laws of Physics cannot be different in different reference frames. Or put another way, Newtonian approaches do not survive a Lorentz transformation (or demand that the speed of causality is infinite instead of c). But the Hamiltonian goes all the way through and is still around in Quantum Mechanics later as an operator acting on the quantum states, as essentially "energy", as we can already see in its roots here as the sum of energies in classical mechanics.
I personally can’t say for Hamiltonian Mechanics but I have worked with Lagrangian Mechanics and it does really help in cases of spring systems. For example if there are multiple masses on springs with dampers, using Newtonian Mechanics might not be the most fun experience but using Lagrangian Mechanics can simplify deriving the differential equation.