I have a question: Why must the m*d/dt( ∂H/ ∂p) + ∂H/ ∂x equal 0? Can that be understood from the equations above, and if so how? The rest is all more than clear. Thanks
@@Yongbangxiang88 Because the net force is equal to the negative derivative of potential energy with respect to position if the system is conservative, which in this case it is. Since Newton's second law (F = ma = m(d^2 x/dt^2)) and the other equation (F = -dU/dx) both give the same magnitude of the net force except with opposite signs in a conservative system, m * d/dt(∂H/∂p) + ∂H/∂x = 0
I have a question about the solution to the differential equation at the 4:00 mark. My understanding is that when you solve for the solution you find C1e^(at)cos(wt) + C2e^(at)sin(wt), where C1 and C2 would be your amplitudes and 'a' and 'b' are the values from the imaginary equation a + bi >> 0 +wi. My question is this: Why are we only using the cosine portion of the solution and not both cos and sin? Is it because the oscillation is only happening along the x-direction? My differential equation textbook(11th edition by Zill, 'a first course in DEs with modeling applications) shows both cos and sin in the solution for free undamped motion. I am a math & physics major so I am trying to figure out why a DE class would utilize the entire solution but Hamiltonian mechanics only uses part of it. Thanks in advance.
The mathematical solution does indeed allow for both portions of the solution. However when you look at the physical system, oscillatory motion is defined by a single sin or cos function. The only difference between the two is the phase difference, but you will not see a physical oscillation where both parts of the solution are present. When you apply the boundary conditions for position and velocity, you will find that one of the solutions will drop out.
That makes complete sense to me. Thank you for clarifying Professor Biezen. I have subscribed to your YT channel, and bookmarked your ilectureonline.com website. I will share with my fellow students.
Sir would it be possible to have some more lecturs on hamiltoniam mechanics and maybe one or two explaining the difference between lagrangian and hamiltonian ?
If we solve problem..with lagrangian and Hamilton result will be same in every cases both proof Newtonian formalism..... Difference is that in lagrangian we take q dot...and in Hamilton we convert q dot into momenta..(p)...but I want to know more difference..plz help me wid that
+Underminded Disguiser Since the equation being solved is F= ma, the way to express this is with a second order differential equation. There are a number of playlists on differential equations if you are interested starting with this one: DIFFERENTIAL EQUATIONS 1 - INTRODUCTION
So why do Hamiltonian AND Lagrangian mechanics exist? I mean, is there any difference between them at the end (the output of using them is the same, isnt it)? It doesn't matter which one do you choose when solving a problem right? Or is it more useful if you solved a specific example with hemiltonian instead of lagrangian or vice versa, Because, if I am not mistaken, they both yield the differential equation x(t)... Thank you
People have always tried to push the understanding of math and science and quite often they have found different ways to get to the same solution. Each method is worth learning to gain that greater understanding. In the end when it comes to solving problems, you pick the method you prefer.
As far as I know, I can tell that lagrangian mechanics is simpler to modelate than newtonian mechanics. Also, it is said that hamiltonian mechanics are also easier than lagrangian for very complex systems (it's worth mentioning that hamiltonians are the way to express mechanics at quantum levels), so you can see that the worst the problem, the more you are inclined to use lagrangian or hamiltonian mechanics, since both are made to make them easier. Note: Those two are made for complex systems. Trying to use them in very simple systems like an ideal parabolic toss or a mass traveling alongside an Edge may result in an overkill, as those lead to "fancy" ways to say _F=ma_.
Hi excellent video, I just didn't understood the part where you rewrite the equation why is m below and where do we take the omega and the amplitude? Could you please clarify this part a little bit Thank you
When you take the partial derivative dH/dp you get dx/dt (velocity). The mass cancels out. Then you take the derivative with respect to time. You should just get d2x/dt2. In the video you show this derivative as m d2x/dt2. Where does the m come from?
Willie,I appreciate you getting back to us. I understand the frustration as we were students once upon a time searching far and wide for anything that could help us understand the seemingly incomprehensible material. Part of the reason why we are putting together these videos (6,200 and counting).
I am unsure but you may need a universal resonance curve which is an approximate symmetric response. Look up natural frequency , resonance, oscillator linewidth and phasenoise,
The potential energy gained by compressing a spring is indeed (1/2) kx^2 See the video: Physics 8 Work, Energy, and Power (4 of 37) Compressing a Spring
Your title indicates this is one of eighteen, but it ends at 3. I find this to be not only annoying but unethical and will complain to utube about this. I just spent an hour trying to find lecture 4. ??I know academics live in a different spacetime then the rest of this but how about a little responsibility.
Our apologies if you wasted time to find the others. Many of our videos are still being developed thus these playlists are in progress and will be completed as time allows. There are just the 2 of us tackling a monumental task to provide free education to students around the world and we have invested MANY thousands of hours doing so. We both work our day jobs and evening jobs providing for our families and do this as a service to the world.
Well I must apologize for what I now see as an overly emotional reaction. It was actually brought about largely by the superb quality of your videos. There is a revolution going on in education and as a retired engineer and night school instructor I am loving it. But much of the videos are just someone following a lecturer as he marches up and down in front of a whiteboard. Yours are not, you present a partially filled board, clearly state your objectives and and are obviously prepared. This effort must require considerable time. I have been watching Suskind's lectures and though I appreciate and admire his work the camera work leaves me almost in teats. One more silly comment. I am a student of history and of science fiction. I believe the work that you are doing will be viewed for centuries. The live expectancy of electronic media, baring disasters (possibly brought on by an unnamed politician) is virtually infinite.I doubt if the Hamiltonian will experience much change. Please take the time to finish your masterpiece. Again I sincerely apologize for my comments. Larry
He is the only professor whom I can follow without difficulties. My hope is to understand all the stuff.
Glad the videos are helpful!
Thanks professor with you the concepts looks very easy
You are welcome. Glad you found our videos. 🙂
Best professor online
I have a question: Why must the m*d/dt( ∂H/ ∂p) + ∂H/ ∂x equal 0? Can that be understood from the equations above, and if so how? The rest is all more than clear. Thanks
im facing that same question too
@@Yongbangxiang88 Because the net force is equal to the negative derivative of potential energy with respect to position if the system is conservative, which in this case it is. Since Newton's second law (F = ma = m(d^2 x/dt^2)) and the other equation (F = -dU/dx) both give the same magnitude of the net force except with opposite signs in a conservative system, m * d/dt(∂H/∂p) + ∂H/∂x = 0
the equation is simply another way of writing F=ma. Take a look at the first video in this series.
I have a question about the solution to the differential equation at the 4:00 mark. My understanding is that when you solve for the solution you find C1e^(at)cos(wt) + C2e^(at)sin(wt), where C1 and C2 would be your amplitudes and 'a' and 'b' are the values from the imaginary equation a + bi >> 0 +wi. My question is this: Why are we only using the cosine portion of the solution and not both cos and sin? Is it because the oscillation is only happening along the x-direction? My differential equation textbook(11th edition by Zill, 'a first course in DEs with modeling applications) shows both cos and sin in the solution for free undamped motion. I am a math & physics major so I am trying to figure out why a DE class would utilize the entire solution but Hamiltonian mechanics only uses part of it. Thanks in advance.
The mathematical solution does indeed allow for both portions of the solution. However when you look at the physical system, oscillatory motion is defined by a single sin or cos function. The only difference between the two is the phase difference, but you will not see a physical oscillation where both parts of the solution are present. When you apply the boundary conditions for position and velocity, you will find that one of the solutions will drop out.
That makes complete sense to me. Thank you for clarifying Professor Biezen. I have subscribed to your YT channel, and bookmarked your ilectureonline.com website. I will share with my fellow students.
Thank you for passing it on.
My question as well.
Sir would it be possible to have some more lecturs on hamiltoniam mechanics and maybe one or two explaining the difference between lagrangian and hamiltonian ?
We plan on doing more as time permits. (We are trying to cover many topics).
If we solve problem..with lagrangian and Hamilton result will be same in every cases both proof Newtonian formalism..... Difference is that in lagrangian we take q dot...and in Hamilton we convert q dot into momenta..(p)...but I want to know more difference..plz help me wid that
Very good lecture Sir. Thanks 🙏🙏🙏🙏
Glad it helped.
Thank you. This was extremely clear!
Great video! Is it possible that you could show us how to derive the first order differential equations as opposed to second order?
+Underminded Disguiser Since the equation being solved is F= ma, the way to express this is with a second order differential equation. There are a number of playlists on differential equations if you are interested starting with this one: DIFFERENTIAL EQUATIONS 1 - INTRODUCTION
Thanks!
So why do Hamiltonian AND Lagrangian mechanics exist? I mean, is there any difference between them at the end (the output of using them is the same, isnt it)? It doesn't matter which one do you choose when solving a problem right? Or is it more useful if you solved a specific example with hemiltonian instead of lagrangian or vice versa, Because, if I am not mistaken, they both yield the differential equation x(t)... Thank you
People have always tried to push the understanding of math and science and quite often they have found different ways to get to the same solution. Each method is worth learning to gain that greater understanding. In the end when it comes to solving problems, you pick the method you prefer.
As far as I know, I can tell that lagrangian mechanics is simpler to modelate than newtonian mechanics. Also, it is said that hamiltonian mechanics are also easier than lagrangian for very complex systems (it's worth mentioning that hamiltonians are the way to express mechanics at quantum levels), so you can see that the worst the problem, the more you are inclined to use lagrangian or hamiltonian mechanics, since both are made to make them easier.
Note: Those two are made for complex systems. Trying to use them in very simple systems like an ideal parabolic toss or a mass traveling alongside an Edge may result in an overkill, as those lead to "fancy" ways to say _F=ma_.
@@HijackedSlang I think the Lagrangian has the advantage that it is lorentz invariant ie you can use it in relativistic systems
a very clear explanation which i really like
Hi excellent video,
I just didn't understood the part where you rewrite the equation why is m below and where do we take the omega and the amplitude?
Could you please clarify this part a little bit
Thank you
What caused to to take those derivates after you wrote down the T + V equations?
As in, how did you know to do dH/dx, dH/dp, and d(dH/dp)/dt?
Yes I have the same question. Has the Hamiltonian been defined in terms of these partial derivatives?
That has to do with the calculus of variations applied to mechanics. Look for Euler-Lagrange formula.
Excellent video series. Thank you for all the help!
Thanks a million, sir.
I'm guessing this is only for ideal oscillators as there is no damping ratio involved?
Correct. Damping is not considered in this example.
What if you have many moving objects that have different momentums and positions? Do you take different deriatives of these?
already got answer: www.physicsforums.com/threads/the-derivative-of-velocity-with-respect-to-a-coordinate.971038/#post-6205505
When you take the partial derivative dH/dp you get dx/dt (velocity). The mass cancels out. Then you take the derivative with respect to time. You should just get d2x/dt2. In the video you show this derivative as
m d2x/dt2. Where does the m come from?
The Hamiltonian equation is
m(d/dt(∂H/∂p)) + ∂H/∂x = 0
The m is built into the equation
thank you so much for the video.
but i want to know what book or source you are lecturing ?
We use many sources.
How can the energy (the Hamiltonian) changes with position
Does that violet the conversation of energy
The energy can change from one form to another form, while keeping the conservation of energy.
I don’t know how to solve the differential at last. Can you explain me.
We have several playlists on differential equations on this channel that show how to solve this type of differential equation and many more.
But isn't the momentum a function of x? Don't you need to differentiate the first term of the hamiltonian as well?
No, this is how the Hamiltonian is set up.
it has explicit dependence only on velocity
well explained, thank you
Glad it was helpful!
sir Biezen can you solve a Coupled double pendulum problem using Lagrangian or Hamiltonian? Thanks
Dr. van Brezen Please note that I apologized for my complaints after you replied but it got buried in the replys. Thankyou
Willie,I appreciate you getting back to us. I understand the frustration as we were students once upon a time searching far and wide for anything that could help us understand the seemingly incomprehensible material. Part of the reason why we are putting together these videos (6,200 and counting).
Thankyou. Being 72 the clock is ticking. So little time , so much beautiful physics. 6,200 videos, wow! Appreciate your taking the time to respond.
Have fun with them. I am still learning every day as well.
Can you convince me that this is applicable in an electric circuit under nonsinusoidal conditions ?
Harmonics in the current provided by a non linear electric load, how can i describe the portion of the energy flow of something like this ?
I am unsure but you may need a universal resonance curve which is an approximate symmetric response. Look up natural frequency , resonance, oscillator linewidth and phasenoise,
How did you take PE (kx^2)/2?
The potential energy gained by compressing a spring is indeed (1/2) kx^2 See the video: Physics 8 Work, Energy, and Power (4 of 37) Compressing a Spring
Thank u very much professor.
You are welcome
Super sekali...
very useful. thank you very much.
superb
helpful video
thxxx much
You're welcome!
Thank you can me pdf clacica
That is something for the future.
Your title indicates this is one of eighteen, but it ends at 3. I find this to be not only annoying but unethical and will complain to utube about this. I just spent an hour trying to find lecture 4. ??I know academics live in a different spacetime then the rest of this but how about a little responsibility.
Our apologies if you wasted time to find the others. Many of our videos are still being developed thus these playlists are in progress and will be completed as time allows. There are just the 2 of us tackling a monumental task to provide free education to students around the world and we have invested MANY thousands of hours doing so. We both work our day jobs and evening jobs providing for our families and do this as a service to the world.
Well I must apologize for what I now see as an overly emotional reaction. It was actually brought about largely by the superb quality of your videos. There is a revolution going on in education and as a retired engineer and night school instructor I am loving it. But much of the videos are just someone following a lecturer as he marches up and down in front of a whiteboard. Yours are not, you present a partially filled board, clearly state your objectives and and are obviously prepared. This effort must require considerable time. I have been watching Suskind's lectures and though I appreciate and admire his work the camera work leaves me almost in teats.
One more silly comment. I am a student of history and of science fiction. I believe the work that you are doing will be viewed for centuries. The live expectancy of electronic media, baring disasters (possibly brought on by an unnamed politician) is virtually infinite.I doubt if the Hamiltonian will experience much change. Please take the time to finish your masterpiece.
Again I sincerely apologize for my comments.
Larry