After studying and teaching physics (I have a Ph.D. in physics from Purdue) for most of my adult life, I can say I am truly learning physics from Prof. V. Balakrishnan.
The Prof is clearly enjoying every moment of it. For the audience, many would be wanting to tear of their hair in sheer frustration! Every word, so aptly chosen, is like 1000 words.
29:00 For anybody interested in the case of U(x) = kx^4, search for Duffing’s equation, Jacobian elliptic functions, and as another method Lindstedt’s Method, which still allows some good approximations of trajectory and period.
Brilliant ideas by a brilliant mind. Great interaction by curious students as well. For anybody who's using these lectures for self study, use Lagrangian and Hamiltonian Mechanics as supplement. If you want, you can send me your email and I can send you a pdf copy of the book. Keep the curiosity alive! Good Luck.
For people who think all this "math" is complex and is not necessary, Von Neumann says: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
+MarthamadaySaamanu I am fifteen, in Italy, and I'm able to understand this easily, not with the velocity of the students, sometimes I have to pause the video and spend less than a minute to think about it, but I think it is just a matter of practice. If the math was difficult, I don't think I would understand this, am I wrong?
+Continuum ST I have taught some of this material to fifteen year olds. Like the variational principles, Lagrangians and Hamiltonians (mainly the principle of least action). It was like an extra class for the interested students. Motivated fifteen year olds generally enjoy these courses. I am sure they can follow the math up to some level. You don't need to follow all of it in one gulp. I keep revisiting these lectures.
Imagination can lead you to creativity. You can analyze a lot of evidence and fail to make sense of it. Sometimes, a spark of nonsenseness is required. I think only imagination can provide that. We´ve seen examples of these in Physics all the time.
9:45 It is common to mark asymptotic approach of phase trajectory to equilibrium point by open circle. This way it is easy to see that it actually never reaches it in finite time, and that there are no trajectory crossings.
@Abhimanohar1 I understand that it is demotivating to watch lectures for which you lack the required background. However, this is the way physics actually works, it is the way physicists think and the way physics is done in the field. Physics is a mathematical discipline, and there is no such thing as "understanding the physics without the mathematics". Susskind's lectures are great but very introductory, and insufficient if you want more from physics than an interesting hobby.
6:57 "Give it just enough energy...." But aren't phase trajectories drawn for autonomous systems ? (Giving just enough energy at t=0 would mean the existence of some force that transfers the energy. This force is time-dependent, since it acts only at t=0)
so whats the problem here i think we give some initial velocity and let the particle move in that potential if the potential is time independent why would the force be time dependent.
Siddhant Rathi oh really😂, thats the fucking problem of you IITiana. You try to prove that you know things instead of having attitude for seeking knowledge.
Some people seem not to understand this is an upper division Analytic Mechanics class. It's taught to people who already have a general physics background and the extensive math Prof. B uses is because there's a wide variety of problems which more "intuitive" methods cannot solve. The math methods developed in this sort of class are also carried over to more advanced classes in Quantum Mechanics or Field Theory--which are definitely not intuitive. If you don't like it then don't be a physicist.
Btw, these examples my seem contrived but they are not. They are showing up everywhere, including quantum mechanics! Basically every potential can be approximated with parabola close to a minimum or maximum, so basically small vibrations and other motions, can be often modelled by harmonic oscillator or these barrier. So you will see it everywhere, including statistical physics, quantum field theory and chaos theory.
I think I know the Susskind lectures on youtube that you are talking about. Those lectures are meant for continuing education people, and aren't suppose to confuse people who do not have the backgrounds right, this one on the other hand, is for future physicists. But, I'm sure that if you actually go to stanford and attend one of the regular classes of Susskind, it should be equally mathematical.
At 8:20, he states that as the particle crawls up the hill, the force becomes smaller and smaller and the particle takes longer and longer to reach to 0. Can somebody explain this?
the force is defined as the gradient of the potential, so for a one dimensional harmonic oscillator, -dV/dx is the force at a point which is the slope at a point, so if you see at the top of the parabola(near the maxima) the slope approaches 0 as if you try to draw a tangent line near those points they tend to go parallel to the x axis which means the slope of the curve (i.e. the gradient of potential) is 0
why v=0 for equilibrium? For equilibrium why not only a=0 condition sufficient? Thats how we use to find min potential or max potential... F=-dU/dx .......and F=0 for critical condition, so, dU/dx=0.... So, do we really need v=0 condition for equilibrium? if we consider v=0 then, what if we consider another inertial frame of ref with some constant velocity? so, can we say this object in equilibrium in this new frame of ref? please help me...
Hello sir... I am doing BSC hons physics course .....ist year . Our ist year syllabus is mechanics and electronics thermal physics etc. .. And in our syllabus, I didn't found Many of the topics covered here...not in our reference books also( kleppner and kolenkov. Feynman lectures of physics etc.) So , do I have to study it just for extra knowledge or is it compulsory for a physics student to cover these topics in BSC hons....??? And which book to follow for these lectures???
@@MohdSameer-rx9gj hello Sameer , these lectures are of the standard of CSIR NET.....for you as a Bsc student it will be quite high standard ....so learn your college references for your BSC is enough ...
+Sarthak Hajirnis V = -0.5mw^2x^2 E = -0.5mw^2a^2 T = E - V = 0.5mw^2(x^2-a^2) Since, 0.5mw^2 is positive, T and (x^2-a^2) got the same sign. So x is restricted in (-inf,-a] v [a,inf) so that T can't < 0, which got "physical meaning".
what is the physical significance of a 'negative energy' in the case of the inverted parabola potential? I can't grasp the concept of a system having a total energy which is negative, can someone elaborate this for me? Thanks!
07bhas I can cite an example.... The gravitational potential energy is negative if the zero of the potential is defined to be at Infinity. In that case, the energy is negative... You can view negative energy as in bound systems
Well basically having positive energy means you can continue your motion in an infinite spacial region. So opposite to that having negative energy implies that your motion is bounded to certain velocities or position values like in the case of orbital motion
Awe-inspiring lecture by Professor Balakrishnan. Terrific clarity of thought and presentation. But I have a comment here: Yes, physics can be explained by mathematics but the understanding of physics that we can enjoy , wonder through nature, and apply for practical purposes is completely absent here. Something like, it is more important I believe to understand the front-end of physics before going into the back-end. I gained a lot of information from this lecture but did not enjoy it.
Nobody really knows how to accurately measure intelligence and/or how to define the relevance of different parts of the brain in science. I've always seen imagination as a way of producing new information, based on previous information, not in a logical way though. Logic is a reduction of info actually, you start from the general to get to a particular conclusion, imagination is the other way around, like having few examples and guess the bigger scenario, well maybe, but your point was not bad
Electric field due to an infinite sheet of charge density sigma is given by (sigma/2*epsilon) which is a constant, therefore a test charge(say positive) located above the sheet would be attracted(for negative sigma) to it with the same force irrespective of its distance from the sheet and the same would happen if the charge is present on the opposite side of the sheet. This makes for an example of a force that is constant and acts in a restoring manner.
If angular frequency is equal to 1 then....... Ellipse would be a circle..... And hence for such situation... Two phase trajectory will intersect..... Am I getting something wrong here....... Please explain
You are again deeply mistaken and heavily shadowed from your ego of "Im correct". When you come out of it you will understand that mental accumen is not about making things complex and aggrandizing nature. It rather allows you to simplify the intricacy. That is the understanding and education I am talking about not increasing human ego by making complicated things and trying to understand them.
After studying and teaching physics (I have a Ph.D. in physics from Purdue) for most of my adult life, I can say I am truly learning physics from Prof. V. Balakrishnan.
Balakrishnan sir is a perfect blend of mathematics rigour and physis brilliance....Hatt's off to you sir
The Prof is clearly enjoying every moment of it. For the audience, many would be wanting to tear of their hair in sheer frustration! Every word, so aptly chosen, is like 1000 words.
I had SO MANY "Ooooohh!!!!" moments during this video.
I feel like I understand how the world works way better than I did before.
I guess Im kinda randomly asking but do anyone know of a good site to watch newly released movies online ?
naturally a physics toughness can be identified easily observing a professor words but here his face is showing how easy the physics is.
One of the best series on classical mechanics. Thankyou very much sir.....
pure joy in listening to him.
29:00 For anybody interested in the case of U(x) = kx^4, search for Duffing’s equation, Jacobian elliptic functions, and as another method Lindstedt’s Method, which still allows some good approximations of trajectory and period.
Will check 🔥
when he said we dont always need maths lets solve it physically.............blown my mind
Brilliant ideas by a brilliant mind. Great interaction by curious students as well. For anybody who's using these lectures for self study, use Lagrangian and Hamiltonian Mechanics as supplement. If you want, you can send me your email and I can send you a pdf copy of the book. Keep the curiosity alive! Good Luck.
Send me a copy ty
Please send me a copy also.
For people who think all this "math" is complex and is not necessary, Von Neumann says: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
+MarthamadaySaamanu I am fifteen, in Italy, and I'm able to understand this easily, not with the velocity of the students, sometimes I have to pause the video and spend less than a minute to think about it, but I think it is just a matter of practice.
If the math was difficult, I don't think I would understand this, am I wrong?
+Continuum ST It's quite impressive that a fifteen year old can understand what's going on here. Have you studied calculus by yourself?
Anand R. Yes, I did.
+Continuum ST I have taught some of this material to fifteen year olds. Like the variational principles, Lagrangians and Hamiltonians (mainly the principle of least action). It was like an extra class for the interested students. Motivated fifteen year olds generally enjoy these courses. I am sure they can follow the math up to some level.
You don't need to follow all of it in one gulp. I keep revisiting these lectures.
You may be a genius. When I was 15 I hadn't heard of Nabla, for example, for another 5 years.
great lecture sir, it was truly a pleasure to watch this
Absolutely poetic!
Never ceases to amaze
Imagination can lead you to creativity. You can analyze a lot of evidence and fail to make sense of it. Sometimes, a spark of nonsenseness is required. I think only imagination can provide that. We´ve seen examples of these in Physics all the time.
last derivation is pure genius
is this undergraduate of a graduate lecture?
I see it need a lot of prerequisete! I like it!
9:45 It is common to mark asymptotic approach of phase trajectory to equilibrium point by open circle. This way it is easy to see that it actually never reaches it in finite time, and that there are no trajectory crossings.
wow what a great lecture....plz also suggest a book to read as well
Thank you sir . sir in 32:06 acceleration is different at different points then who does the time is equal.
@Abhimanohar1
I understand that it is demotivating to watch lectures for which you lack the required background. However, this is the way physics actually works, it is the way physicists think and the way physics is done in the field. Physics is a mathematical discipline, and there is no such thing as "understanding the physics without the mathematics". Susskind's lectures are great but very introductory, and insufficient if you want more from physics than an interesting hobby.
really cool introduction to the video!!!
100% true
Does anyone know whether NPTEL will hand out online degrees at some point?
6:57
"Give it just enough energy...."
But aren't phase trajectories drawn for autonomous systems ? (Giving just enough energy at t=0 would mean the existence of some force that transfers the energy. This force is time-dependent, since it acts only at t=0)
you can only speak on comment section if you would have asked sir balakrishna, he would have shut you up instantly with your silly arguments
so whats the problem here i think we give some initial velocity and let the particle move in that potential if the potential is time independent why would the force be time dependent.
I think, Professor is emphasising on what can happen if it has just enough energy at t=0, and not worrying about how he acquired it.
@@saianvesh7637 Yeah thanks.. I figured that out later
Siddhant Rathi oh really😂, thats the fucking problem of you IITiana. You try to prove that you know things instead of having attitude for seeking knowledge.
Great lecture!!
Some people seem not to understand this is an upper division Analytic Mechanics class. It's taught to people who already have a general physics background and the extensive math Prof. B uses is because there's a wide variety of problems which more "intuitive" methods cannot solve. The math methods developed in this sort of class are also carried over to more advanced classes in Quantum Mechanics or Field Theory--which are definitely not intuitive. If you don't like it then don't be a physicist.
Are these lectures also given in front of a class?
yes
Smart teaching .....
Btw, these examples my seem contrived but they are not. They are showing up everywhere, including quantum mechanics! Basically every potential can be approximated with parabola close to a minimum or maximum, so basically small vibrations and other motions, can be often modelled by harmonic oscillator or these barrier. So you will see it everywhere, including statistical physics, quantum field theory and chaos theory.
Can anyone suggest me a book which goes with this lecture series ??
I think I know the Susskind lectures on youtube that you are talking about. Those lectures are meant for continuing education people, and aren't suppose to confuse people who do not have the backgrounds right, this one on the other hand, is for future physicists. But, I'm sure that if you actually go to stanford and attend one of the regular classes of Susskind, it should be equally mathematical.
At 8:20, he states that as the particle crawls up the hill, the force becomes smaller and smaller and the particle takes longer and longer to reach to 0. Can somebody explain this?
the force is defined as the gradient of the potential, so for a one dimensional harmonic oscillator, -dV/dx is the force at a point which is the slope at a point, so if you see at the top of the parabola(near the maxima) the slope approaches 0 as if you try to draw a tangent line near those points they tend to go parallel to the x axis which means the slope of the curve (i.e. the gradient of potential) is 0
Great lecture
Nptel is the best online learning place for all students
@krishtube Without the mathematics, there is no application.
What is the Phase space of the 3D Harmonic oscillator? What is the dimension of that?
6 dimensional
Draw in 3 sheet
X px
Y py
Z pz in different sheet.
Phase space is 3d but the curve is 1d
Where would I get explanation of constants of motion in this series?
Lagrangian and Hamiltonian Mechanics by M.G. Calkin**
why v=0 for equilibrium? For equilibrium why not only a=0 condition sufficient? Thats how we use to find min potential or max potential... F=-dU/dx .......and F=0 for critical condition, so, dU/dx=0.... So, do we really need v=0 condition for equilibrium? if we consider v=0 then, what if we consider another inertial frame of ref with some constant velocity? so, can we say this object in equilibrium in this new frame of ref? please help me...
Could anyone suggest what all mathematical courses one should pursue to supplement this one?
how to draw ellipsoid in six dimensional phase space in case of three dimensional harmonic oscillator?
Can’t do it
best proff
Will anyone please tell me that for which course are these lectures meant for....BSC or Msc or even higher?
It's Msc standard but those who do the honor's course they study this in their Bsc
Hello sir... I am doing BSC hons physics course .....ist year .
Our ist year syllabus is mechanics and electronics thermal physics etc. ..
And in our syllabus, I didn't found Many of the topics covered here...not in our reference books also( kleppner and kolenkov. Feynman lectures of physics etc.)
So , do I have to study it just for extra knowledge or is it compulsory for a physics student to cover these topics in BSC hons....???
And which book to follow for these lectures???
@@MohdSameer-rx9gj hello Sameer , these lectures are of the standard of CSIR NET.....for you as a Bsc student it will be quite high standard ....so learn your college references for your BSC is enough ...
Ok.....I will come back to these lectures once I complete my reference books....
Thanks.
Which reference book you are studying?
@5:51 in the graph... why that region is in accessible? Please someone provide an elaborated explanation.
+Sarthak Hajirnis
V = -0.5mw^2x^2
E = -0.5mw^2a^2
T = E - V = 0.5mw^2(x^2-a^2)
Since, 0.5mw^2 is positive, T and (x^2-a^2) got the same sign.
So x is restricted in (-inf,-a] v [a,inf) so that T can't < 0, which got "physical meaning".
Is he taking classes for MSc. programme?
what is the physical significance of a 'negative energy' in the case of the inverted parabola potential? I can't grasp the concept of a system having a total energy which is negative, can someone elaborate this for me? Thanks!
07bhas I can cite an example.... The gravitational potential energy is negative if the zero of the potential is defined to be at Infinity. In that case, the energy is negative... You can view negative energy as in bound systems
Well basically having positive energy means you can continue your motion in an infinite spacial region. So opposite to that having negative energy implies that your motion is bounded to certain velocities or position values like in the case of orbital motion
at 7.40 ,why does the direction of the graph upward? anyone explain pls. i think it should be downward tooo.!
Awe-inspiring lecture by Professor Balakrishnan. Terrific clarity of thought and presentation. But I have a comment here: Yes, physics can be explained by mathematics but the understanding of physics that we can enjoy , wonder through nature, and apply for practical purposes is completely absent here. Something like, it is more important I believe to understand the front-end of physics before going into the back-end. I gained a lot of information from this lecture but did not enjoy it.
I don't understand it's people who dislike it or it's RUclips which dislikes on its own
Educational
All was fine but I didn't get how it was defined at the end (T2=R3)....I mean how all the arguments led to the final conclusion.
undergraduate. we do this stuff in 2nd year. physics department
Konstantinos Meichanetzidis This is an undergraduate course lecture !
we too ;-)
Nobody really knows how to accurately measure intelligence and/or how to define the relevance of different parts of the brain in science. I've always seen imagination as a way of producing new information, based on previous information, not in a logical way though. Logic is a reduction of info actually, you start from the general to get to a particular conclusion, imagination is the other way around, like having few examples and guess the bigger scenario, well maybe, but your point was not bad
Its deduction. Inductive reasoning generalizes.
Sir when are live class of you
Sir, what will happen if potential is complex one ??
by 'complex' what do you mean? the complex no.s or the complexity in the expression of potential?
Energy is always a real number
Undergraduate student here. I think a "complex" potential has no scope within classical theory. as per my limited knowledge, it appears in QMech.
I would not say complicated math but It definitely takes a bit more of thinking
At @47:00 there is example of infinite charge sheet can anyone plzz elaborate it
Electric field due to an infinite sheet of charge density sigma is given by (sigma/2*epsilon) which is a constant, therefore a test charge(say positive) located above the sheet would be attracted(for negative sigma) to it with the same force irrespective of its distance from the sheet and the same would happen if the charge is present on the opposite side of the sheet. This makes for an example of a force that is constant and acts in a restoring manner.
@@abeerarora8017 thanks
If angular frequency is equal to 1 then....... Ellipse would be a circle..... And hence for such situation... Two phase trajectory will intersect.....
Am I getting something wrong here....... Please explain
How two face trajectories will intersect?
how can i get DVD of these lecture series
the world has changed so uch since you wrote this some 12 years ago. Hope you're doing good. :)
i dont understand what the fuck is going on but i like it
Is this for Undergrad students or Grad students?
I think its Grad (maybe M.Sc) Theres no way this is undergrad. If it is, goddam the level for undergrad is too damn high.
@@TheGamingg33k its undergrad actually ....
This is no way undergrad course.
You are again deeply mistaken and heavily shadowed from your ego of "Im correct". When you come out of it you will understand that mental accumen is not about making things complex and aggrandizing nature. It rather allows you to simplify the intricacy. That is the understanding and education I am talking about not increasing human ego by making complicated things and trying to understand them.
iss vedio pe comment karne ki meri aukat bhi nahi hai..............
Hinduism bro....the opposite of creepy