Thanks to your videos I started studying physics and maths again when I was 30, seven years later and I am about to start a masters degree in physics. Thanks again, you really did help me a lot.
Seriously, this is one of the best videos I have ever seen. By far the most lucid and comprehensible introduction to analytical mechanics available. Thank you very much.
Excellent and magnificent! I studied and passed my classical mechanics exams and can apply the Lagrangian and Hamiltonian formulations for solving simple problems like Harmonic oscillator, planetary motion etc. But I always knew the logic and methods used to derive the Lagrange equation in almost every book was too difficult to grasp and therefore a bit vague. Most writers make the situation too difficult at a very early stage of their explanation by introducing the subtle concepts of virtual work, dAlembert’s principle, generalized coordinates etc making it very difficult to follow for someone like me. This is a great teacher, given me the feeling of how the analytical formulation treats mechanical systems from a deeper level of reasoning. Same applies to his ‘Dirac Notation of Quantum Mechanics’ what I found very beneficial too.
Hey its 7 years later, how is your physics career going? R u still doing physics? R u a physicist now? What do you do? Im just interested lmao sorry for any inconviniences
@@Sasukej2004 Hi thanks for remembering. Well Physics is too difficult for my average brain. I have been continuing with learning physics though. But I don’t think it will take me anywhere, as I am not a teacher but a software engineer.
I accept the points you have made in your comments today. Mea Culpa. In mitigation, I refer to my reason for producing these videos. They are intended as a relatively easy way into the subject. They are not intended to be rigorous, particularly not the maths! I wanted to offer something to those who find it difficult to understand the basic concepts. Once that has been done, there are other sources which offer the detailed rigour, altho they also tend to be much more complex.
This guy is awesome and this channel Definetively should get attention again, I don't know what he works as but he could help thousands of College studends if he started amplifying his content.
You have given so much to human kind. I struggle to keep up with retaining the steps but in general it makes sense. THANK YOU! Please keep teaching. i am very greatful to see and hear each lecture you provide. You are a gift to us all. You don't change need to change how you present the knowledge. Understanding comes over time. i think of how plato taught his students. We now have the ability to review the lecture multiple times until it sinks in. From a very greatful older student. William G Russell
Thanks. No problem. Not hurt at all. Gave me an opportunity to explain more widely about how I approach the vids and why they aren't as detailed as, say, a Leonard Susskind video. And I welcome contributions on the comments section which will help other readers and expand the detail given. Indeed there have been some discussions which go way beyond my knowledge. All good wishes.
" A basic.. " seems not just having been given, but very carefully created by only such teacher/professor who have been well aware of the value, "The Basic." This lecturer might be one of one thousand those in this field. Xcellent, very.
I have watched a couple of videos that were roughly two hours in length and neither were as elegant and as easy to understand as this. Professor Susskind should really put these on his playlist!!!
Because Xb is a variable and we are trying to identify the minimum action associated with a path between Xa and Xc and which travels through varying intermediary Xb positions.
Great, I knew I could rely on you for a clear explanation. I've come here for an explanation of the Lagrangian because Prof. Susskind glosses over what the hell it is in his classical mechanics lectures. But his audiences seem to be largely composed of grandstanding idiots and I wonder how they can follow any of what he says judging by their questions.
you are mistaking "idiot" with less educated. This means you are the idiot. And not everyone has rich parents like you and can afford not working like you.
Not really.Sometimes they do their own research to an extent of nailing the topic like 90% of the time before theyll ever attend the lecture.So some of the “questions” are more or less raised so as to double check they’re right.
I came from Susskins' videos, he covers the lagrangian in 10 seconds. Not helpful. I finally stumbled upon yours and finally understand L=KE-PE!!!!!!!!!!
Apart from learning many other extremely useful + interesting things I also learnt that Analytical mechanics is something in which you cannot become good in just 38 mins 26 sec. Best explanation though.
Thanks for the great video! I'd love if you could do more stuff on Analytical Mechanics, I'm reading it now and definitely struggling to understand, this has helped loads!
Kinetic energy is the amount of work that has been done to something to make it go a certain speed. When you get on a highway and reach a velocity, V, your engine has done 1/2 m V^2 joules of work. You have 1/2 m V^2 joules KE
Lagrangian, hmm I've heard about that. Principle of least action, ok. Euler Lagrange equation, uhhhh well. Ha....miltonian, ahhhhh. That is so informative despite there were some stumblings in your video. Thank you for giving me a preview or an intro about this a few weeks before my actual lectures.
Why the principle of minimum action? Ive heard it is in fact the principle of stationary action and that could coincide with a minumum but not necessarilly. It could be a maximum or some sort of saddle point.
Thanks very much!! you are awesome. Now I can understand every much clearly... And also you speak very well and clearly as well. Im from overseas and even that I did understand everything. Keep doing this, Is very useful.. Thanks again
I have hoped you would have shown or given an insight as to why the Action must be minimized in mechanical trajectories in the first place. You took it here as an axiom or something given. Or do things get originally derived backwards, i.e. start with conservation of energy and you get to Action being minimum?
Thanks again professor...your channel is one of the bests i know in youtube...very good video...it's a quite complicated subject but the video is helping me out on understanding La Grange...hope one day be able to figure out the full picture of this...:-)
At 1.32 and 12.07, when you draw the parabola (trajectory) of the moving body, the speed mentionned should be "u" and not "v" because that's the way you defined the initial velocity.
Hi, DrPhysics you continually say that s is distance, but that is not true because distance is scalar and the work done is the dot product of two vectors, Force and the displacement. So if it was distance and you moved 1 metre and then back to the original position, you have moved 2 metres (scalar) BUT what we are REALLY saying is the change in position (displacement)... Otherwise your videos are very good.
first of all i want to say that ur channel is great....i love physics and i am definately gonna see all of ur videos....could you tell me in what order to see the playlists???
At 11:52 was that the derivation of Newton's law of gravitation.If yes.................... YES !YEAH! HAPPINESS. I was looking for that from quite a long time. THANK YOU VERY MUCH DR. YOU ARE A GREAT TEACHER
28' into the video, the Euler-Lagrange is parachuted without anything like a proper justification. This said, the first 5 minutes of the video are worth listening to, because conservation of energy is proved very well.
Thanks for your video! However, at 23:26 I think you should do a partial derivative instead: dL/dVb x dVb/dXb. The dVb/dXb gives you an extra term of 1/epsilon and -1/epsilon when it comes to Vc and that mathematically explains the minus sign. Also the 1/epsilon is essential to to group the dL/dV terms later on in a d/dt (dL/dV) term.
Hey I completely agree with your comment! ... could you maybe explain why dVb/dXb is equal to 1/epsilon ? I'm thinking dVb/dXb = 1/E so that dVb = dXb/E which makes sense since E(epsilon) is a small change in time, so its like dV=dX/dt... Is your reasoning the same? Thanks again ( I know its a very old comment)
Dan Akelom Hi. I think that is one way of seeing it. For point C do not forget what "DrPhysicsA" mentions which is if you have a positive delta in Xb the velocity decreases and therefore dVc/dXb = -1/E. Despite the fact that I think you are correct in your way of thinking, that was not how I got dVb/dXb = 1/E. I have simply done it in a pure mathematical fashion. The Lagragian depends on Vb and on its turn Vb depends on Xb. So you need to apply the chain rule: dL/dXb = dL/dVb * dVb/dXb. SInce we don't have an expression for the Lagragian we leave dL/dVb as it is, but we do have an expression for Vb: Vb= (Xb-Xa)/E therefore we can easily find what is dVb/dXb, and that is 1/E (Xa and E are regarded as constants when you're doing the derivative). Since Vc= (Xc-Xb)/E you get dVc/dXb=-1/E . If you put all together you get: -(dL/dVc - dL/dVb)/E Recalling the definition of derivative: d/dt(f(t))@t0= limit when E->0 of ( f(t0+E) - f(t0) ) /E we can see that: -(dL/dVc - dL/dVb)/E = -d/dt(dL/dVb) I hope this helped...
justpaulo of course! I applied the chain rule, but just didn't get 1/E the way you did (which is as you said 'purely mathematical'), very helpful method Thanks!
Potential energy is "stuff" that can do work. When you buy gas you are actually buying Chemical Potential Energy to make your car do the work required to get you from point a to point b
Thanks for this excellent video! So Newton's differential formulae can be derived from the integral Principal of Least Action. You introduced the latter as an experimental fact: Action A is minimal if determined along the real path as opposed to any other non-real path. However, I have always felt slightly uncomfortable with the meaning of the Lagrangian itself. You even mentioned "L is NOT T+V", probably to not have us confuse L with the (more familiar) total energy. So, what *is* L? Can we somehow get a feeling of what the Lagrangian does? I like to think of L (or rather -L) as the margin in which the system can distribute its resources at any given time. Like V-T being the value of not-yet converted potential energy, sort of a measure of possibilities of what may come next: Either have the ball (and V) rise up higher and lose T or vice versa. Does this make sense...
Thanks for this job. I don't agree when you say that E kin - B is not conservative. It is since it stays the same fir initial and final state. This is not because there is a minus that it is not conserved. Also it the way you declare that u (which is -B) is potential energy is artificial. At about 11.00 you apply the formula f= - dU/dx but for the gravitationnal potentiel energy you forgot to take in account de minus sign.
No that I'm complaining. Great work Dr Physics! Much clearer than many other explanations. I'm a stickler for these kinds of details (they're kinda important).
+Ninja Trash I believe he should be using partial derivatives there. Since 1/2 m v^2 is not explicitly a function of x (only x dot), the partial derivative evaluates to 0.
Something I don't really get and would be very grateful if someone could explain for me - at 25:45 you have everything in the brackets multiplied by epsilon, then in the next line you describe what happens as epsilon tends to zero. But wouldn't that mean everything in the bracket just becomes zero, if you're multiplying the brackets by zero? I may have misunderstood how you use limits. Thanks for the vids, especially these long and more indepth ones, they are absolutely fantastic!
There is a deep mathematical error @ 38:26 The derivative w. r. t Xb can not be equal to the derivative w. r. T Vb I know this is a simplification for the sake of deriving the final concept but I think this will lead to mathematical impeguity
in about 20 minutes, you took for the first lagrangian x for b for the part from a to b of the path but from b to c you took x for c. why? thanks alot for the valuable work
Well do you mind posting some sort of description to that math or a link to help analyze how you went from one line to the other? even though this is supposed to be a simple video, it would really help if some of us could also see the bigger picture. I, for one, have seen all of college calc (MechE major).
DrPhysics you are a hero! Ive been reading this subject for almost a month, and then i found this video, and learned it in less than 40 minutes!
Thanks for kind comments. In order to keep away from the really complex maths I simplified things at this point to argue the principle.
Thanks to your videos I started studying physics and maths again when I was 30, seven years later and I am about to start a masters degree in physics. Thanks again, you really did help me a lot.
Seriously, this is one of the best videos I have ever seen. By far the most lucid and comprehensible introduction to analytical mechanics available. Thank you very much.
Excellent and magnificent!
I studied and passed my classical mechanics exams and can apply the Lagrangian and Hamiltonian formulations for solving simple problems like Harmonic oscillator, planetary motion etc. But I always knew the logic and methods used to derive the Lagrange equation in almost every book was too difficult to grasp and therefore a bit vague. Most writers make the situation too difficult at a very early stage of their explanation by introducing the subtle concepts of virtual work, dAlembert’s principle, generalized coordinates etc making it very difficult to follow for someone like me. This is a great teacher, given me the feeling of how the analytical formulation treats mechanical systems from a deeper level of reasoning. Same applies to his ‘Dirac Notation of Quantum Mechanics’ what I found very beneficial too.
Hey its 7 years later, how is your physics career going? R u still doing physics? R u a physicist now? What do you do? Im just interested lmao sorry for any inconviniences
@@Sasukej2004 Hi thanks for remembering. Well Physics is too difficult for my average brain. I have been continuing with learning physics though. But I don’t think it will take me anywhere, as I am not a teacher but a software engineer.
@@tagorechandmeah425 o then y did u studied physics in uni?
@@tagorechandmeah425 Also software engineering is hard too ur awesome, u hav an awesome brain i dont think its average
I accept the points you have made in your comments today. Mea Culpa. In mitigation, I refer to my reason for producing these videos. They are intended as a relatively easy way into the subject. They are not intended to be rigorous, particularly not the maths! I wanted to offer something to those who find it difficult to understand the basic concepts. Once that has been done, there are other sources which offer the detailed rigour, altho they also tend to be much more complex.
This guy is awesome and this channel Definetively should get attention again, I don't know what he works as but he could help thousands of College studends if he started amplifying his content.
You have given so much to human kind. I struggle to keep up with retaining the steps but in general it makes sense. THANK YOU! Please keep teaching. i am very greatful to see and hear each lecture you provide. You are a gift to us all. You don't change need to change how you present the knowledge. Understanding comes over time. i think of how plato taught his students. We now have the ability to review the lecture multiple times until it sinks in.
From a very greatful older student.
William G Russell
amazing lecture... right on track, no going out of the way to explain something unnecessary and all very straightforward to follow. thank you
Thanks. Glad to have been of some help.
Are you on any of the social networks Professor?
Thanks. No problem. Not hurt at all. Gave me an opportunity to explain more widely about how I approach the vids and why they aren't as detailed as, say, a Leonard Susskind video. And I welcome contributions on the comments section which will help other readers and expand the detail given. Indeed there have been some discussions which go way beyond my knowledge. All good wishes.
The concept of L = KE - PE has been lucidly explained! Nowhere I found such a nice explanation!
Thanks. I am most grateful. I have added an annotation to clarify the position.
" A basic.. " seems not just having been given, but very carefully created by only such teacher/professor who have been well aware of the value, "The Basic." This lecturer might be one of one thousand those in this field. Xcellent, very.
What a legend! You got ME completely understanding in under 40 mins, and I am an idiot! Best explanation ever.
I have watched a couple of videos that were roughly two hours in length and neither were as elegant and as easy to understand as this.
Professor Susskind should really put these on his playlist!!!
Because Xb is a variable and we are trying to identify the minimum action associated with a path between Xa and Xc and which travels through varying intermediary Xb positions.
Time to start reading more of my calculus textbook
You made it easy to understand. Thank you ever so much. Your derivation was magnificent.
Great, I knew I could rely on you for a clear explanation. I've come here for an explanation of the Lagrangian because Prof. Susskind glosses over what the hell it is in his classical mechanics lectures. But his audiences seem to be largely composed of grandstanding idiots and I wonder how they can follow any of what he says judging by their questions.
you are mistaking "idiot" with less educated. This means you are the idiot. And not everyone has rich parents like you and can afford not working like you.
@@danielschwegler5220 What a load of assumptions you've made. Your response doesn't follow the comment at all, completely illogical.
Not really.Sometimes they do their own research to an extent of nailing the topic like 90% of the time before theyll ever attend the lecture.So some of the “questions” are more or less raised so as to double check they’re right.
I AM LITERALLY HERE FOR THE SAME REASON!!!!!!!!!!!!
Brilliant, I love it.
Thank you so much.
Thank you for your videos. They play a significant part in contributing to my studies and I recommended you to my lecturer today for inspiration.
I wanted to throw my keyboard at the screen when you pulled the Hamiltonian out of thin air. That was beautiful.
Have you tried Prof Leonard Susskind's lectures on Classical Mechanics on TH-cam. He covers the maths in more depth.
I came from Susskins' videos, he covers the lagrangian in 10 seconds. Not helpful. I finally stumbled upon yours and finally understand L=KE-PE!!!!!!!!!!
Wow this has to be my favorite video of yours, you have taught me the foundations and notation to a lot iof interesting and important physics
The only thing that i wanted to know was, what is Hamiltonian and finally i understood it. Thank you
Brilliant explanation.Clear and concise.
This video helped me pass my A-Level physics exam!
Apart from learning many other extremely useful + interesting things I also learnt that Analytical mechanics is something in which you cannot become good in just 38 mins 26 sec. Best explanation though.
Sir, can you please make a video, showing us some applications of analytical mechanics and what are it's advantages over it's Newtonian counterpart .
I love this channel!!!!!!!!!!
You are great at explaining basic and complex physics....
Fantastic video. It gives the context, making the Wikipedia pages on the topic so much easier to understand.
Sir, you are doing God's work
Thank you sir!
Awesome as always.
Please never stop doing these videos.
There is so much more to cover. :)
Thanks for the great video! I'd love if you could do more stuff on Analytical Mechanics, I'm reading it now and definitely struggling to understand, this has helped loads!
fantastic video and fantastic channel. thank you for taking the time. You sound like the teacher every student would dream to have!
Kinetic energy is the amount of work that has been done to something to make it go a certain speed. When you get on a highway and reach a velocity, V, your engine has done 1/2 m V^2 joules of work. You have 1/2 m V^2 joules KE
Great explanation
Starting Analytical Methods this Fall, thanks for the headstart!
25:40 Why? I don't get how do you deduced the euler-lagrange equation?
Thank you so much for the amazing lecture, now that I understand what is L and H.
Lagrangian, hmm I've heard about that. Principle of least action, ok. Euler Lagrange equation, uhhhh well. Ha....miltonian, ahhhhh.
That is so informative despite there were some stumblings in your video. Thank you for giving me a preview or an intro about this a few weeks before my actual lectures.
Man these demonstrations were a proverbial Atomic bomb for my mind. VERY awesome! Keep up the good work Doc.
thank you so much. appreciate the work you do in making these videos. you have helped me alot in understanding physics in another way.
Why the principle of minimum action? Ive heard it is in fact the principle of stationary action and that could coincide with a minumum but not necessarilly. It could be a maximum or some sort of saddle point.
Thanks very much!! you are awesome. Now I can understand every much clearly... And also you speak very well and clearly as well. Im from overseas and even that I did understand everything. Keep doing this, Is very useful.. Thanks again
I have hoped you would have shown or given an insight as to why the Action must be minimized in mechanical trajectories in the first place. You took it here as an axiom or something given. Or do things get originally derived backwards, i.e. start with conservation of energy and you get to Action being minimum?
thanks for something this much simplified.
Thanks again professor...your channel is one of the bests i know in youtube...very good video...it's a quite complicated subject but the video is helping me out on understanding La Grange...hope one day be able to figure out the full picture of this...:-)
Wonderful lecture. Thank you!
The dot product is a scalar, but yes, displacement takes direction into account.
At 1.32 and 12.07, when you draw the parabola (trajectory) of the moving body, the speed mentionned should be "u" and not "v" because that's the way you defined the initial velocity.
Great, thank you!!! this will help with my Acoustics classes! :)
Hi, DrPhysics you continually say that s is distance, but that is not true because distance is scalar and the work done is the dot product of two vectors, Force and the displacement. So if it was distance and you moved 1 metre and then back to the original position, you have moved 2 metres (scalar) BUT what we are REALLY saying is the change in position (displacement)... Otherwise your videos are very good.
very usefull and your pronunciation of english helped me as italian
Thank you very much !!!! you are really the BEST :D
first of all i want to say that ur channel is great....i love physics and i am definately gonna see all of ur videos....could you tell me in what order to see the playlists???
As always- excellent!
I'v seen Walter Lewin's lectures on class mech, but have yet to finish looking through them all. I'll give Susskind's lectures a shot. Thanks!
Hi, i wonder if system's kinetic energy is constant , the system is not work to do?
Wow great video! Very helpful and super understandable explanations!
Absolutely brilliant! Thank you :)
is the U at 8.30 a different variable from initial velocity U in the Suvat eqaution?
Yes, from memory, the U he uses @8:30 is potential energy, which is usually capital U. Initial velocity is usually lowercase u.
At 11:52 was that the derivation of Newton's law of gravitation.If yes....................
YES !YEAH! HAPPINESS. I was looking for that from quite a long time. THANK YOU VERY MUCH DR. YOU ARE A GREAT TEACHER
Samarth Sai *necroposting* No it wasn't, he literally took it from the gravitational potential
I listen to this for background noise while I game... I should probably start the series over sometime and actually go through the math with him..
Can you just add two integrals (from a to b + b to c) to get action?
28' into the video, the Euler-Lagrange is parachuted without anything like a proper justification.
This said, the first 5 minutes of the video are worth listening to, because conservation of energy is proved very well.
What a fantastic tutorial. Thanks a lot.
Thanks for your video!
However, at 23:26 I think you should do a partial derivative instead: dL/dVb x dVb/dXb. The dVb/dXb gives you an extra term of 1/epsilon and -1/epsilon when it comes to Vc and that mathematically explains the minus sign. Also the 1/epsilon is essential to to group the dL/dV terms later on in a d/dt (dL/dV) term.
Hey I completely agree with your comment! ... could you maybe explain why dVb/dXb is equal to 1/epsilon ? I'm thinking dVb/dXb = 1/E so that dVb = dXb/E which makes sense since E(epsilon) is a small change in time, so its like
dV=dX/dt... Is your reasoning the same? Thanks again ( I know its a very old comment)
Dan Akelom
Hi. I think that is one way of seeing it. For point C do not forget what "DrPhysicsA" mentions which is if you have a positive delta in Xb the velocity decreases and therefore dVc/dXb = -1/E.
Despite the fact that I think you are correct in your way of thinking, that was not how I got dVb/dXb = 1/E. I have simply done it in a pure mathematical fashion. The Lagragian depends on Vb and on its turn Vb depends on Xb. So you need to apply the chain rule: dL/dXb = dL/dVb * dVb/dXb. SInce we don't have an expression for the Lagragian we leave dL/dVb as it is, but we do have an expression for Vb:
Vb= (Xb-Xa)/E
therefore we can easily find what is dVb/dXb, and that is 1/E (Xa and E are regarded as constants when you're doing the derivative).
Since Vc= (Xc-Xb)/E you get dVc/dXb=-1/E . If you put all together you get:
-(dL/dVc - dL/dVb)/E
Recalling the definition of derivative:
d/dt(f(t))@t0= limit when E->0 of ( f(t0+E) - f(t0) ) /E
we can see that:
-(dL/dVc - dL/dVb)/E = -d/dt(dL/dVb)
I hope this helped...
justpaulo of course! I applied the chain rule, but just didn't get 1/E the way you did (which is as you said 'purely mathematical'), very helpful method Thanks!
It always confuses me when left- and right-hand-side don't match in dimension: 21:17, bottom.
Potential energy is "stuff" that can do work. When you buy gas you are actually buying Chemical Potential Energy to make your car do the work required to get you from point a to point b
You are an amazing teacher.Please suggest a introductory text book.I tried Goldstein it's too heavy.Thanks for the video.
simply great as usual!
that was cool. thanks from Morocco
Excellent excellent overview!
Thanks for this excellent video! So Newton's differential formulae can be derived from the integral Principal of Least Action. You introduced the latter as an experimental fact: Action A is minimal if determined along the real path as opposed to any other non-real path. However, I have always felt slightly uncomfortable with the meaning of the Lagrangian itself. You even mentioned "L is NOT T+V", probably to not have us confuse L with the (more familiar) total energy. So, what *is* L? Can we somehow get a feeling of what the Lagrangian does?
I like to think of L (or rather -L) as the margin in which the system can distribute its resources at any given time. Like V-T being the value of not-yet converted potential energy, sort of a measure of possibilities of what may come next: Either have the ball (and V) rise up higher and lose T or vice versa. Does this make sense...
The only thing I still don't understand is why use T and V for kinetic energy and potential energy instead of K and U?
*this is an amazing explanation*
Thanks for this job.
I don't agree when you say that E kin - B is not conservative. It is since it stays the same fir initial and final state. This is not because there is a minus that it is not conserved.
Also it the way you declare that u (which is -B) is potential energy is artificial.
At about 11.00 you apply the formula f= - dU/dx but for the gravitationnal potentiel energy you forgot to take in account de minus sign.
The dL/dV terms should have a factor of 1/epsilon by the chain rule. This gives the time derivative inside the larger bracket.
No that I'm complaining. Great work Dr Physics! Much clearer than many other explanations. I'm a stickler for these kinds of details (they're kinda important).
A Great video.
Maybe it's a dumb question.
At 27:30 why d/dx(1/2 m v^2) is 0?
v = dx/dt
How d/dx(dx/dt)^2 is 0?
+Ninja Trash I believe he should be using partial derivatives there. Since 1/2 m v^2 is not explicitly a function of x (only x dot), the partial derivative evaluates to 0.
I worship you.
Something I don't really get and would be very grateful if someone could explain for me - at 25:45 you have everything in the brackets multiplied by epsilon, then in the next line you describe what happens as epsilon tends to zero. But wouldn't that mean everything in the bracket just becomes zero, if you're multiplying the brackets by zero? I may have misunderstood how you use limits. Thanks for the vids, especially these long and more indepth ones, they are absolutely fantastic!
Can anybody explain to me the difference between "Physics: Classical Mechanics" and Engineering: Dynamics"?
Bravo Sir , If you expained some examples to simplified that concepts !
At 24.53, the way you calculate dA/dx b is very particular, could you make it clearer ?
Can i ask a question? : At around the 22':30" time why you didn't write A= L(Xa) + L (Xb) + L (Xc)?
Well done DrPhysicsA
Very helpful. Thanks.
Analytical mechanics makes me feel like I'm on a hot date.
Not that sort of Action dude.
There is a deep mathematical error @ 38:26
The derivative w. r. t Xb can not be equal to the derivative w. r. T Vb I know this is a simplification for the sake of deriving the final concept but I think this will lead to mathematical impeguity
Great video ! Really informative.
But it would be so much better if it was at least 720p... Really a shame. But nonetheless, great video.
Thanks. I choose the resolution mainly based on the Time it takes to upload the video.
I am very, very bad at memorizing, so l could just theoretically imagine it
me too )
thanks so much I am grateful
As it tends to zero is different then being zero. He is talking about the derivative rather than the actual = to 0.
sir can you make video about this with problem example solution?
11:15 Typo: F = -(d/dx)mgx
Minus sign was missing.
in about 20 minutes, you took for the first lagrangian x for b for the part from a to b of the path but from b to c you took x for c. why? thanks alot for the valuable work
I took 2 paths. a to b and then b to c. I'm looking at the position at the end of each path and the velocity for each path (i.e. distance over time).
Thank you!
Well do you mind posting some sort of description to that math or a link to help analyze how you went from one line to the other? even though this is supposed to be a simple video, it would really help if some of us could also see the bigger picture. I, for one, have seen all of college calc (MechE major).
hi Dr has also video subjects conservation laws, central force ...
Have continued?? This will help me a lot
Thanks
At around 11:20 , shouldn't F = -mg ?
Yes. Altho I was only calculating magnitudes. Generally PE is negative so F is positive.
Got it, thanks for clarifying. :)
DrPhysicsA But why is L = T - U, can this be derived from D'Alembert's principle?