What I can see and feel in Prof.V.Balakrishnan's words is a pure, absolute and deeply precise understanding of physics, mathematics and their interplay..............Hats off....! :)
this is a much higher quality production than stanford's one. notice that there are more than one cameras (possibly at least 3) and they track the speaker, blackboard (when needed) as well as the listeners. the videographers are quite skilled in shooting such videos, in contrast to the stanford-susskind's producers/videographers, who seem quite amateurish
Never before have I seen the marriage between mathematics and mechanics demonstrated so brilliantly. This professor has reignited my passion for physics, it's really inspiring, this University should be proud of the quality and high standards.
Since he is a professor in one of the top institute in India IIT Madras (IIT Bombay is first) You can expect the standards .... but actually only 1% of the applicants are selected for these institutes ... There are around 1 Million ppl who take JEE ( entrance exams for IITs and world's toughest entrance examination) out of which only 10k are selected :( But we are still happy to have professors like him .. And yeah a fact about him is that his children are now professors in MIT .
Brillant lecture, thanks a lot! The very important fact that q, q dot and time are independent parameters defining, e.x., applied forces, can be illustrated in the following examples: a) F(t)=F_0*sin(omega*t) b) F(q,t)=-kq + F_0*sin(omega*t) c) F(q,q_dot,t)=e* q_dot*B - kq + F_0*sin(omega*t)
From 9:13 one could have continued on with geometric way of reasoning rather than with less elegant linear VS quadratic algebraic logic. Tetrahedron is a solid with least number of corners. All solids can be treated as assemblies of tetrahedrons. So one tetrahedron glued to rest of the body full of infinitesimal tetrahedrons one tetrahedron can mimic the whole body. Applying the logic up until then, the total dof is= 4 corners x 3 dof - 4C2 = 12 - 6 = 6 dof
45:20 the orientation of the phase trajectory direction can be determined here even simpler. At q=0 and q' =y, the y is positive (at the top), so the q must be increasing. So the arrow at that point is toward increasing q, so clockwise.
37:38 the non intersecting principle of phase trajectory is only true if the system is autonomous. I.e. when the potential or force doesn't depend explicitly on time. If it depends on time, the you could in principle extend phase space to also include additional axis, and of course then the phase trajectories do not intersect, or even close, even if the motion is "periodic" per se. It does have a connection to energy conservation. Autonomous systems are time translation invariant, so via the Nether's theorem, there is a conserved quantity called Energy. The phase trajectories are basically lines of constant energy.
I like this professor, he does a good job at elaborately explaining things, as oposed to other profesors, which don't take the time to fully glorify physics.
28:10 where he explains that a particle can even depend on higher order terms of position like acceleration is simply amazing, which is missed all most all books.(I have mentioned "all most" as leaving the possibility of books saying that ,but I have never come across).
well there is a NPTEL site in India for all nptel lectures so largely people watch there. also some students struggle in pure english so they prefer lectures with mix of languages where explanation is in Hindi or other regional languages. no doubt his lecture are perfect. whoever comes across his lectures, they'll all agree to that.
Aha. This guy is great. In the quantum one he just stuttered out in amazement: you guys haven't taken complex analysis yet? I great professor to intrigue a motivated student but, though, oh god, if he taught any of the slack***es at my college. He'd have
The prayer, in the beginning, comforts the abyss of my heart with a deep sense of realization that all nature is of God's grace and it is more yet to be discovered in the field of science.
Texts that goes along the same line of this series : 1. Ordinary differential equation V.I.Arnold. 2. Mathematical methods of classical mechanics V.I.Arnold. 3. Mechanics, Landau.
Hi, I have a question about the degrees of freedom topic, introduced at 5:04. If you start with one particle in R3, it has 3 degrees of freedom. If you add a second particle and fix their positions relative to each other, it is helpful to define a coordinate system in the frame of reference of the relative position vector of those two particles. This is due to the fact that you can define one basis vector to be collinear with that relative position vector. If you do that, then one of those degrees of freedom becomes redundant, leaving you with 5 degrees of freedom that can describe the full behaviour (translation, rotation, and some combination) of that 2 particle system. I have done some work on this, and with three particles forming a fixed triangle, the situation becomes more complicated. It is best to work in 4 separate coordinate systems, and draw the triangle and vectors. You have one local coordinate system for each two particle, fixed line segment. You then superimpose the three line segments, each with their own coordinate system, into a fixed triangle. To the full triangle, assign a global coordinate system. This global coordinate system has 6(3)-3(1) = 15 basis vectors. However, 6 of those basis vectors are redundant. It can then be argued that there are a total of 9 basis vectors for the three particle system, because some combination of those vectors' magnitudes, applied to their respective particles, can describe the full constrained motion (translation and rotation, or some combination). Does anyone have any thoughts on this, or a method to construct some sort of proof of this? I don't think that 6 degrees of freedom, for a 3 particle fixed system, is sufficient to describe all the possible motions of that triangle (translation, rotation, or some combination) without deforming the triangle. Any elaborations on this topic would be welcome.
We calculate the degree of freedom by introducing particles to this system one by one. For two particles system, the degree of freedom is 5, 3 for the first one and 2 for the second one. To understand it, think of the first particle to be at the origin. The second particle in terms of spherical coordinates (r, phi, theta). Here r is constrained since the distance between both particles is a constant. Hence the second particle has two degrees of freedom. Since, the first particle need not be at the origin but instead can be at any coordinate say (x,y,z). Hence, the total becomes 5. For 3 particles system (triangle), we similarly construct it particle by particle. Till the second particle has been added to the system, the degree of freedom is 5. When the third one is added it becomes 6. As in a triangle, the perpendicular distance between a vertex and the opposite side (known as altitude) is constant. Here the third vertex is the third particle that is being added to the system and altitude is a point on the line joining two particles. So basically the distance between the side and particle is constrained, and the particle can only rotate about the axis/line joining the first and the second particle. The rotation about this axis can be by an angle, say theta, which implies that we have a single degree of freedom. Hence, the total becomes 6.
@devrj12 I think he's saying that, to rotate the body-fixed coordinate system into the "absolute" coordinate system, you need to do a single rotation around a particular axis. It takes two d.o.f.'s to specify the axis. These could be just the "theta" and "phi" of ordinary polar coordinates, which he calls "latitude and longitude. (Indeed, a latitude and longitude will get you to any desired axis on the sphere.) Then, you need a third number the the rotation about that axis. Or three total.
falling peace of chalk is not rotating when it's falling ... you dont need the other 3 dof's because when the body is not rotating the falling system behaves as if all of it was at a the center of mass ... at lest i think thats the case, i can't guarantee ...
You said 2 interacting Particles have 6 degrees of freedom. 2 particles joined by a rigid shaft has 5 degrees of freedom because of the constraint of constant distance between them. The rigid shaft is an electromagnetic and quantum interaction. This electromagnetic cum quantum interaction reduces the degree of freedom by one. But other interactions don't seem to do so as it is said that 2 interacting(say gravity) particles have 6 degrees of freedom. What is the condition on the interaction which reduces the degree of freedom by one in one case whereas in other cases like gravity it doesn't.
At 5:07 sir, you say it gives 5 independent coordinates but sir, only the distance between point one and 2 is fixed not the vector. Then why is 6th coordinate still a dependent coordinate.. isn’t it somewhat free ? Since it CAN move in a circle ... Same is the case with 3 particles ... why should there be only 7 independent coordinates ? ....
Classical theory of radiation has pathologies like violation of causal response and runaway behaviors. When we assume that Lagrangian not be a function of acceleration or higher derivatives of q, are we not implicitly demanding causal behavior for classical systems ?
So the rigid body always has 6 degres of freedom, I can kinda understand, that there is no difference between 80 particles and 81 particles in terms of degrees of freedom, however is there a possibility to proof this result?
Evidently not. please! Point particle does not have an angular momentum (the "other" 3 degrees of freedom) and, of course formal proof is possible. Is an exercise in Euclidean geometry, but they don't teach it at elementary school any more. All these straight (unmarked) edge and (collapsing, that is unsuitable to mark distances) compass constructions are enough to prove it. (with some projective stuff for 3d, because we have no access to drawing in 4d)
to be more precise, adding one particle to a system of 3 particles rigidly connected adds 3 degrees of freedom to the system, but adding additional three constraints - the distances from an added point (let it be) "k" to "a", "b", "c" of a triangle. The constraints then are |ak|=const, |bk|=const and |ck|=const which neatly cuts the number of degrees of freedom back to 6. The process remains true for higher dimensions. We "augmented" triangle to tetrahedron. Triangle is a 2-simplex, tetrahedron is a 3-simplex, 4-simplex is called a 5-cell, which one can see easily on its planar projection. One can count its rotational degrees of freedom in 4 dimensions on such a projection (with a good dose of imagination or with some propping up with colours and computer animation). Wikipedia just says that symplectic relations emerge naturally in classical mechanics. It's not so hard to see it.
I have a doubt, a self intersecting phase trajectory (q, v) simple means that the system has repeated coordinates and velocity at another point of time as well, is that impossible? does not feels like, though the argument by Prof is sound and I am definitely missing sth
If at that particular co-ordinate (position, velocity); if you don't change the force, the next point is unique but not two different outcomes. Imagine a planet revolving, It repeats co-ordinates (comes to same point with same velocity) but does not change trajectory second time.
who is more important: Prof. Balakrishnan or the students? I just can't understand what's so special in the students that the camera is focused at them instead of the professor.
Walter Lewin also gives great lectures on this topic with many cool demonstrations and way better penmanship. Professor Lewin can work chalk like you wouldn't believe.
i know i am late but say there is some intitial velocity at x=0, then the particle will obviously move say dx distance at that instant now the force on the particle is -ve of the derivative of potential and derivative of potential (i.e. the slope) is in this case itself -ve and then the force will be positive(+ve x direction) and will at each point will push it towards infinity
It means that only one independent coordinate will be enough to specify any position on the curve uniquely. All other coordinates will be dependent on the independent one. A phase trajectory is essentially a curve. If you have solved line integrals then you can understand what I am talking about. If not, then try to look into line integrals section in chapter 6 I guess, of Mathematical methods book by Mary L Boas.
What I can see and feel in Prof.V.Balakrishnan's words is a pure, absolute and deeply precise understanding of physics, mathematics and their interplay..............Hats off....! :)
this is a much higher quality production than stanford's one. notice that there are more than one cameras (possibly at least 3) and they track the speaker, blackboard (when needed) as well as the listeners. the videographers are quite skilled in shooting such videos, in contrast to the stanford-susskind's producers/videographers, who seem quite amateurish
susskind and this are for very different audience as well
This University standard of teaching is incredible.
Never before have I seen the marriage between mathematics and mechanics demonstrated so brilliantly. This professor has reignited my passion for physics, it's really inspiring, this University should be proud of the quality and high standards.
Since he is a professor in one of the top institute in India IIT Madras (IIT Bombay is first) You can expect the standards .... but actually only 1% of the applicants are selected for these institutes ... There are around 1 Million ppl who take JEE ( entrance exams for IITs and world's toughest entrance examination) out of which only 10k are selected :( But we are still happy to have professors like him .. And yeah a fact about him is that his children are now professors in MIT .
@@beyondhumanrange6196 that doesn't surprise me at all. I hope the tradition never stops
@@owen7185 Am sorry which tradition are you talking about ... Never ending realm of good professors or the JEE ??
@@beyondhumanrange6196 both
@@beyondhumanrange6196 I am not debating anything here, I like what I see, that's all and not only this subject
Brillant lecture, thanks a lot!
The very important fact that q, q dot and time are independent parameters defining, e.x., applied forces, can be illustrated in the following examples:
a) F(t)=F_0*sin(omega*t)
b) F(q,t)=-kq + F_0*sin(omega*t)
c) F(q,q_dot,t)=e* q_dot*B - kq + F_0*sin(omega*t)
I totally agree. I wish so hard they uploaded lectures on Modern Physics, Electromagnetism of QFT taught from Balakrishnan!
Did he teach those chapters as well?
From 9:13 one could have continued on with geometric way of reasoning rather than with less elegant linear VS quadratic algebraic logic. Tetrahedron is a solid with least number of corners. All solids can be treated as assemblies of tetrahedrons. So one tetrahedron glued to rest of the body full of infinitesimal tetrahedrons one tetrahedron can mimic the whole body. Applying the logic up until then, the total dof is= 4 corners x 3 dof - 4C2 = 12 - 6 = 6 dof
Its great to see over 50,000 people are watching and learning about physics. Thanks to Prof.V.Balakrishnan and of course RUclips!
That made me giggle like a little kid LOL. Man, I love this guy. Wish I had profs like this...
Greatest lectures ever since the birth of internet.
45:20 the orientation of the phase trajectory direction can be determined here even simpler. At q=0 and q' =y, the y is positive (at the top), so the q must be increasing. So the arrow at that point is toward increasing q, so clockwise.
Thank you for this outstanding lecture series. you are the only hero for me besides Dr. Walter lewin . You two make the best of young minds.
And Professor Gilbert Strang (M.I.T.) 😊🙏🏽✨
@@ozzyfromspace Yes . His lectures on quantum mechanics and linear algebra helped me a lot.☺️
Prof. R. Shankar's two series of Yale Lectures on undergraduate physics on RUclips are also excellent.
25:21...a valid question and a pin-point accurate answer by Prof. Balki🔥
This is the deepest part of this lecture.
Thank you Prof. V. Balakrishnan for such wonderfull lecture.
37:38 the non intersecting principle of phase trajectory is only true if the system is autonomous. I.e. when the potential or force doesn't depend explicitly on time. If it depends on time, the you could in principle extend phase space to also include additional axis, and of course then the phase trajectories do not intersect, or even close, even if the motion is "periodic" per se. It does have a connection to energy conservation. Autonomous systems are time translation invariant, so via the Nether's theorem, there is a conserved quantity called Energy. The phase trajectories are basically lines of constant energy.
I like this professor, he does a good job at elaborately explaining things, as oposed to other profesors, which don't take the time to fully glorify physics.
28:10 where he explains that a particle can even depend on higher order terms of position like acceleration is simply amazing, which is missed all most all books.(I have mentioned "all most" as leaving the possibility of books saying that ,but I have never come across).
Thank you professor for this great lecture.
Prof. Balkrishna Sir's deep understanding is awesome👌
The way he talks is so convincing
Sir you have given physics lovers a true taste of physics
Strange so few likes for these lectures which are close to perfection. The students in India alone should raise it over 100K, no?
well there is a NPTEL site in India for all nptel lectures so largely people watch there. also some students struggle in pure english so they prefer lectures with mix of languages where explanation is in Hindi or other regional languages.
no doubt his lecture are perfect. whoever comes across his lectures, they'll all agree to that.
@Dalit Shiv Yep, and only 1.9K likes. Less than 1% !!
Great lecture! Thanks Prof. Balakrishnan!
great lecture,, cleared many of my doubts
To me personally these lectures are better than Susskind's.
totally agree
Yes
Your taste and understanding totally sucks.
It means that you cant understand susskind properly
@@balasujithpotineni8184 Maturity = 100
sir,thank you for showing english titles,bcz it creats interest!
Aha. This guy is great. In the quantum one he just stuttered out in amazement: you guys haven't taken complex analysis yet? I great professor to intrigue a motivated student but, though, oh god, if he taught any of the slack***es at my college. He'd have
Ajay, if you expand and simplify, you get N(N-1)/2
@minasso Yes, he approximated the chalk to a point particle. You are correct that in reality the chalk is a rigid body and should have 6 dof.
what a beautiful teacher!the teaching is just so engaging!
He enjoys teaching a lot and the students benefit.
What a teaching....Calm cool
Like sitting in a pleasant breeze , watching lush greens
The prayer, in the beginning, comforts the abyss of my heart with a deep sense of realization that all nature is of God's grace and it is more yet to be discovered in the field of science.
This is science lecture and don't include God here
And to be more clear there is nothing called God here
Very correctly said Hemanth😄😄
@@adityadubey9565 yes. 😁
What are the words?
Glad to have professor like you 😊😊
A very good lecture of one decade later it is a video of 2009 so it's matter at that time uploading a video is very big thing
Sir, position vs momentum space is phase space. Position vs velocity is state space.
🙏Please update all the courses of Professor Balki, especially the quantum physics course
simply a wonderful way of teaching!!
still watching on 19th january, 2017
15th sept of 2019
Yahi dekhna , kabhi selection nhi hoga inki theory padhne se
Me in March 2 2020
@@subrahmanyamsubbu6001 if you making a notes ....sir veidos plz share my email address Ankitajoshi2971995@gmail.com
@shashank gaur when did he say 2 particles, he is saying that particle can move in a plane which means the particle has now 2 degrees of freedom
A living God! \m/
Ajay, number of possible combinations of 2 objects in a set of N objects is NC2, which can be written as N!/2!(N-2)!
Thank you, Sir. Thank you for clearing the basics knowledge. 😁
Texts that goes along the same line of this series : 1. Ordinary differential equation V.I.Arnold. 2. Mathematical methods of classical mechanics V.I.Arnold. 3. Mechanics, Landau.
Thank u
Are these books sufficient for more into self study along with these lectires?
@@Manish-uk2ow these books are very compact, rigorous and hard, i suggest get more reference books
a. 6:15
b. 15:21
c. 17:34
d: 20:14
e. 22:57
f. 25:18
g. 35:31
😢😢(wiping tears) his not so beautiful handwriting, gave me the hope I needed 😇😇
Never in my life I feel so amase to listen
Hi,
I have a question about the degrees of freedom topic, introduced at 5:04. If you start with one particle in R3, it has 3 degrees of freedom.
If you add a second particle and fix their positions relative to each other, it is helpful to define a coordinate system in the frame of reference of the relative position vector of those two particles. This is due to the fact that you can define one basis vector to be collinear with that relative position vector. If you do that, then one of those degrees of freedom becomes redundant, leaving you with 5 degrees of freedom that can describe the full behaviour (translation, rotation, and some combination) of that 2 particle system.
I have done some work on this, and with three particles forming a fixed triangle, the situation becomes more complicated. It is best to work in 4 separate coordinate systems, and draw the triangle and vectors.
You have one local coordinate system for each two particle, fixed line segment. You then superimpose the three line segments, each with their own coordinate system, into a fixed triangle.
To the full triangle, assign a global coordinate system. This global coordinate system has 6(3)-3(1) = 15 basis vectors. However, 6 of those basis vectors are redundant.
It can then be argued that there are a total of 9 basis vectors for the three particle system, because some combination of those vectors' magnitudes, applied to their respective particles, can describe the full constrained motion (translation and rotation, or some combination).
Does anyone have any thoughts on this, or a method to construct some sort of proof of this?
I don't think that 6 degrees of freedom, for a 3 particle fixed system, is sufficient to describe all the possible motions of that triangle (translation, rotation, or some combination) without deforming the triangle.
Any elaborations on this topic would be welcome.
We calculate the degree of freedom by introducing particles to this system one by one. For two particles system, the degree of freedom is 5, 3 for the first one and 2 for the second one.
To understand it, think of the first particle to be at the origin. The second particle in terms of spherical coordinates (r, phi, theta). Here r is constrained since the distance between both particles is a constant. Hence the second particle has two degrees of freedom.
Since, the first particle need not be at the origin but instead can be at any coordinate say (x,y,z). Hence, the total becomes 5.
For 3 particles system (triangle), we similarly construct it particle by particle. Till the second particle has been added to the system, the degree of freedom is 5. When the third one is added it becomes 6. As in a triangle, the perpendicular distance between a vertex and the opposite side (known as altitude) is constant. Here the third vertex is the third particle that is being added to the system and altitude is a point on the line joining two particles. So basically the distance between the side and particle is constrained, and the particle can only rotate about the axis/line joining the first and the second particle. The rotation about this axis can be by an angle, say theta, which implies that we have a single degree of freedom. Hence, the total becomes 6.
@devrj12 I think he's saying that, to rotate the body-fixed coordinate system into the "absolute" coordinate system, you need to do a single rotation around a particular axis. It takes two d.o.f.'s to specify the axis. These could be just the "theta" and "phi" of ordinary polar coordinates, which he calls "latitude and longitude. (Indeed, a latitude and longitude will get you to any desired axis on the sphere.) Then, you need a third number the the rotation about that axis. Or three total.
amazing ......video ....prof. v balkrishna...
very good English, much better then one of ... some profs in USA.
falling peace of chalk is not rotating when it's falling ... you dont need the other 3 dof's because when the body is not rotating the falling system behaves as if all of it was at a the center of mass ... at lest i think thats the case, i can't guarantee ...
You said 2 interacting Particles have 6 degrees of freedom. 2 particles joined by a rigid shaft has 5 degrees of freedom because of the constraint of constant distance between them. The rigid shaft is an electromagnetic and quantum interaction. This electromagnetic cum quantum interaction reduces the degree of freedom by one. But other interactions don't seem to do so as it is said that 2 interacting(say gravity) particles have 6 degrees of freedom. What is the condition on the interaction which reduces the degree of freedom by one in one case whereas in other cases like gravity it doesn't.
At 5:07 sir, you say it gives 5 independent coordinates but sir, only the distance between point one and 2 is fixed not the vector. Then why is 6th coordinate still a dependent coordinate.. isn’t it somewhat free ? Since it CAN move in a circle ...
Same is the case with 3 particles ... why should there be only 7 independent coordinates ? ....
how could you be late to this class? 7:57
When were these lectures given?
Also, does anyone have the problem sets corresponding to these lectures?
I need the question set too, the lecture was given at IIT Madras, India
@@theawantikamishra Go to the newer NPTEL website
Classical theory of radiation has pathologies like violation of causal response and runaway behaviors. When we assume that Lagrangian not be a function of acceleration or higher derivatives of q, are we not implicitly demanding causal behavior for classical systems ?
So the rigid body always has 6 degres of freedom, I can kinda understand, that there is no difference between 80 particles and 81 particles in terms of degrees of freedom, however is there a possibility to proof this result?
Evidently not. please! Point particle does not have an angular momentum (the "other" 3 degrees of freedom) and, of course formal proof is possible. Is an exercise in Euclidean geometry, but they don't teach it at elementary school any more. All these straight (unmarked) edge and (collapsing, that is unsuitable to mark distances) compass constructions are enough to prove it. (with some projective stuff for 3d, because we have no access to drawing in 4d)
to be more precise, adding one particle to a system of 3 particles rigidly connected adds 3 degrees of freedom to the system, but adding additional three constraints - the distances from an added point (let it be) "k" to "a", "b", "c" of a triangle. The constraints then are |ak|=const, |bk|=const and |ck|=const which neatly cuts the number of degrees of freedom back to 6. The process remains true for higher dimensions. We "augmented" triangle to tetrahedron. Triangle is a 2-simplex, tetrahedron is a 3-simplex, 4-simplex is called a 5-cell, which one can see easily on its planar projection. One can count its rotational degrees of freedom in 4 dimensions on such a projection (with a good dose of imagination or with some propping up with colours and computer animation). Wikipedia just says that symplectic relations emerge naturally in classical mechanics. It's not so hard to see it.
Brilliant, greatest lecture.
this is wonderful lecture
Very true, degrees of freedom must come first
Great lecture
Brilliant!!!
Thanks a lot sir
Is it possible to get the lecture notes, the prescribed text and the homeworks set, to get the full benefit of the course?
19:58 the chalk has 3 degrees of freedom, and the rigid body on the board has 6. Why?
The chalk (and any 3D object) has 6 degree of freedom. A point has three degree of freedom.
point has degree of freedom 3 as spin kinetic energy is negligible due to very small moment of inertia..
I have a doubt, a self intersecting phase trajectory (q, v) simple means that the system has repeated coordinates and velocity at another point of time as well, is that impossible? does not feels like, though the argument by Prof is sound and I am definitely missing sth
If at that particular co-ordinate (position, velocity); if you don't change the force, the next point is unique but not two different outcomes. Imagine a planet revolving, It repeats co-ordinates (comes to same point with same velocity) but does not change trajectory second time.
Love your video's. Is there an accompanying text?
Why the name "phase space"?.
Its very weird.
I agree with you.
Can someone tell me the text prof is following ( if he is following one)?
If a particle oscillating in vertically downward motion.still there are three degrees of freedom?
who is more important: Prof. Balakrishnan or the students? I just can't understand what's so special in the students that the camera is focused at them instead of the professor.
Thank you
Why is the quality of video bad ?
did less girls used to study physics back then ?
is this for m tech please reply
Msc
Mind blowing sir😍😍😍😍
Walter Lewin also gives great lectures on this topic with many cool demonstrations and way better penmanship. Professor Lewin can work chalk like you wouldn't believe.
Prof Lewin was fired by MIT for being involved in inappropriate behaviour towards women on campus
@@parthasur6018 Online sexual harassment? Did you hear what he said online that got him in trouble?
@@parthasur6018 ruclips.net/video/raurl4s0pjU/видео.html
bit of advice take 8.03 mit (diffrential equation) before coming here
At 56:55 "the particle will go downhill if we give it some positive velocity", can somebody explain why the particle would go like that?
i know i am late but say there is some intitial velocity at x=0, then the particle will obviously move say dx distance at that instant now the force on the particle is -ve of the derivative of potential and derivative of potential (i.e. the slope) is in this case itself -ve and then the force will be positive(+ve x direction) and will at each point will push it towards infinity
Mess is great.
Got u Sir..😌
i like the intro video >:?
U can have dof in negative
I couldn't get at that trajectory part of harmonic oscillator...that elliptical part...
16:06 - Why have they slowed down the frame rate to half ?
Are 'q' and 'q double dots' independent of time?
yes.. before solving the problem
superb
Feb 2021
google gives advantages to institutions that publish their work on youtube. this channel is not a standard one.
Can some one help me with what Prof. means by what he say at around 51:20 about phase trajectory being one dimensional...
Any references would also be help.
It means that only one independent coordinate will be enough to specify any position on the curve uniquely. All other coordinates will be dependent on the independent one. A phase trajectory is essentially a curve. If you have solved line integrals then you can understand what I am talking about. If not, then try to look into line integrals section in chapter 6 I guess, of Mathematical methods book by Mary L Boas.
R those for bsc
can someone please tell me some references to these lectures?
For which class were these lectures delivered?
MSc (Physics)
how can he put online video that have more than 10 minutes?
Bhai me abhi preparation kar rha hu jee ki
Wonderful lecture. Why girls are in the back ?
So as not to offend Muslim viewers?
You know how "upperty" (some) Musalman are at times (Im sure)
LambrettaFunk what's with being a dick... he was just asking
Keep out of this white boy, this is an on going thousand year old discussion....
tokamak So much for the "religion of peice" Ha-Ha-Ha-Ha!!!!
LambrettaFunk You're ALSO a moron, huh? (Puzzle on this statement for a few hours.)
Watching in 2018
thank you geez i love you guys
Watching in 2020
what book is he following ?
I think books are following him. ,😀