Analytical Mechanics

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  • เผยแพร่เมื่อ 29 ต.ค. 2024

ความคิดเห็น • 164

  • @ficolossale
    @ficolossale 10 ปีที่แล้ว +24

    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!

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว +15

    Thanks for kind comments. In order to keep away from the really complex maths I simplified things at this point to argue the principle.

    • @CHEESYhairyGASH
      @CHEESYhairyGASH 4 หลายเดือนก่อน +1

      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.

  • @orchidion7634
    @orchidion7634 10 ปีที่แล้ว +14

    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.

  • @tagorechandmeah425
    @tagorechandmeah425 10 ปีที่แล้ว +18

    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.

    • @Sasukej2004
      @Sasukej2004 3 ปีที่แล้ว

      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

    • @tagorechandmeah425
      @tagorechandmeah425 3 ปีที่แล้ว

      @@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.

    • @Sasukej2004
      @Sasukej2004 3 ปีที่แล้ว

      @@tagorechandmeah425 o then y did u studied physics in uni?

    • @Sasukej2004
      @Sasukej2004 3 ปีที่แล้ว

      @@tagorechandmeah425 Also software engineering is hard too ur awesome, u hav an awesome brain i dont think its average

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว +9

    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.

  • @eraimattei
    @eraimattei 5 ปีที่แล้ว +2

    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.

  • @billrussell3955
    @billrussell3955 7 ปีที่แล้ว +1

    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

  • @jessesinger4790
    @jessesinger4790 7 ปีที่แล้ว +1

    amazing lecture... right on track, no going out of the way to explain something unnecessary and all very straightforward to follow. thank you

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว +11

    Thanks. Glad to have been of some help.

    • @sibongumusaws9551
      @sibongumusaws9551 3 ปีที่แล้ว

      Are you on any of the social networks Professor?

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว

    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.

  • @rajthewise
    @rajthewise 3 ปีที่แล้ว

    The concept of L = KE - PE has been lucidly explained! Nowhere I found such a nice explanation!

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว +2

    Thanks. I am most grateful. I have added an annotation to clarify the position.

  • @yujc1
    @yujc1 8 ปีที่แล้ว

    " 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.

  • @oldpariah
    @oldpariah 5 ปีที่แล้ว +1

    What a legend! You got ME completely understanding in under 40 mins, and I am an idiot! Best explanation ever.

    • @lwskiner
      @lwskiner 5 ปีที่แล้ว +1

      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!!!

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว

    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.

  • @merlinthegreat100
    @merlinthegreat100 9 ปีที่แล้ว +9

    Time to start reading more of my calculus textbook

  • @thomasblackwell9507
    @thomasblackwell9507 3 ปีที่แล้ว +1

    You made it easy to understand. Thank you ever so much. Your derivation was magnificent.

  • @stonestreaker
    @stonestreaker 11 ปีที่แล้ว +42

    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.

    • @danielschwegler5220
      @danielschwegler5220 4 ปีที่แล้ว +5

      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.

    • @Mogwai88
      @Mogwai88 4 ปีที่แล้ว +6

      @@danielschwegler5220 What a load of assumptions you've made. Your response doesn't follow the comment at all, completely illogical.

    • @chenlecong9938
      @chenlecong9938 4 ปีที่แล้ว +1

      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.

    • @my_unreasonably_long_username
      @my_unreasonably_long_username 3 ปีที่แล้ว +1

      I AM LITERALLY HERE FOR THE SAME REASON!!!!!!!!!!!!

  • @charliearmour1628
    @charliearmour1628 2 ปีที่แล้ว +1

    Brilliant, I love it.
    Thank you so much.

  • @austinfahrenheit3191
    @austinfahrenheit3191 11 ปีที่แล้ว +1

    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.

  • @Saki630
    @Saki630 10 ปีที่แล้ว

    I wanted to throw my keyboard at the screen when you pulled the Hamiltonian out of thin air. That was beautiful.

  • @DrPhysicsA
    @DrPhysicsA  11 ปีที่แล้ว +4

    Have you tried Prof Leonard Susskind's lectures on Classical Mechanics on TH-cam. He covers the maths in more depth.

    • @my_unreasonably_long_username
      @my_unreasonably_long_username 3 ปีที่แล้ว

      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!!!!!!!!!!

  • @ramansb1213
    @ramansb1213 11 ปีที่แล้ว +2

    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

  • @HariPrasadindependantphysicist
    @HariPrasadindependantphysicist 9 ปีที่แล้ว +1

    The only thing that i wanted to know was, what is Hamiltonian and finally i understood it. Thank you

  • @vincewise855
    @vincewise855 10 ปีที่แล้ว +1

    Brilliant explanation.Clear and concise.

  • @quantumbro827
    @quantumbro827 ปีที่แล้ว

    This video helped me pass my A-Level physics exam!

  • @samarthsai9530
    @samarthsai9530 7 ปีที่แล้ว

    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.

  • @avirupdey7565
    @avirupdey7565 6 ปีที่แล้ว +4

    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 .

  • @Federico282
    @Federico282 11 ปีที่แล้ว +1

    I love this channel!!!!!!!!!!
    You are great at explaining basic and complex physics....

  • @danielnolan5994
    @danielnolan5994 11 ปีที่แล้ว

    Fantastic video. It gives the context, making the Wikipedia pages on the topic so much easier to understand.

  • @mannacharya4088
    @mannacharya4088 4 ปีที่แล้ว +1

    Sir, you are doing God's work

  • @Frogcleaner
    @Frogcleaner 11 ปีที่แล้ว +2

    Thank you sir!
    Awesome as always.
    Please never stop doing these videos.
    There is so much more to cover. :)

  • @MrBobbyArcher
    @MrBobbyArcher 10 ปีที่แล้ว +1

    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!

  • @micpax1
    @micpax1 8 ปีที่แล้ว

    fantastic video and fantastic channel. thank you for taking the time. You sound like the teacher every student would dream to have!

  • @trentvaughn687
    @trentvaughn687 11 ปีที่แล้ว +1

    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

  • @DrAtomics
    @DrAtomics 3 ปีที่แล้ว

    Starting Analytical Methods this Fall, thanks for the headstart!

  • @rodrigoappendino
    @rodrigoappendino 6 ปีที่แล้ว +1

    25:40 Why? I don't get how do you deduced the euler-lagrange equation?

  • @maheshkansakar9007
    @maheshkansakar9007 2 ปีที่แล้ว

    Thank you so much for the amazing lecture, now that I understand what is L and H.

  • @daniello2147
    @daniello2147 5 ปีที่แล้ว

    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.

  • @caiopumar
    @caiopumar 11 ปีที่แล้ว

    Man these demonstrations were a proverbial Atomic bomb for my mind. VERY awesome! Keep up the good work Doc.

  • @mohamedsaid-rd5sb
    @mohamedsaid-rd5sb 11 ปีที่แล้ว

    thank you so much. appreciate the work you do in making these videos. you have helped me alot in understanding physics in another way.

  • @dekippiesip
    @dekippiesip 11 ปีที่แล้ว +2

    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.

  • @kuidsh
    @kuidsh 11 ปีที่แล้ว

    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

  • @Ma7m9d
    @Ma7m9d 9 ปีที่แล้ว

    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?

  • @shradhachawla6414
    @shradhachawla6414 6 ปีที่แล้ว

    thanks for something this much simplified.

  • @FelipeZucchetti
    @FelipeZucchetti 11 ปีที่แล้ว +1

    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...:-)

  • @aabraham6145
    @aabraham6145 8 ปีที่แล้ว +1

    Wonderful lecture. Thank you!

  • @willfeav
    @willfeav 11 ปีที่แล้ว +1

    The dot product is a scalar, but yes, displacement takes direction into account.

  • @chriscross1152
    @chriscross1152 11 ปีที่แล้ว

    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.

  • @Yerfdog1
    @Yerfdog1 10 ปีที่แล้ว +1

    Great, thank you!!! this will help with my Acoustics classes! :)

  • @thinkscientifically7119
    @thinkscientifically7119 11 ปีที่แล้ว +1

    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.

  • @faustogadani4582
    @faustogadani4582 6 ปีที่แล้ว

    very usefull and your pronunciation of english helped me as italian

  • @hassanizaid3772
    @hassanizaid3772 10 ปีที่แล้ว +2

    Thank you very much !!!! you are really the BEST :D

  • @ΠαυλοςΛασκος
    @ΠαυλοςΛασκος 8 ปีที่แล้ว +1

    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???

  • @exxzxxe
    @exxzxxe 2 ปีที่แล้ว

    As always- excellent!

  • @RbtV92
    @RbtV92 11 ปีที่แล้ว

    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!

  • @niyameddinmemmedov9067
    @niyameddinmemmedov9067 4 ปีที่แล้ว

    Hi, i wonder if system's kinetic energy is constant , the system is not work to do?

  • @JannikPitt
    @JannikPitt 8 ปีที่แล้ว

    Wow great video! Very helpful and super understandable explanations!

  • @StephenRayner
    @StephenRayner 9 ปีที่แล้ว +1

    Absolutely brilliant! Thank you :)

  • @AhmadAli-kv2ho
    @AhmadAli-kv2ho 3 ปีที่แล้ว

    is the U at 8.30 a different variable from initial velocity U in the Suvat eqaution?

    • @jamalbingowings6003
      @jamalbingowings6003 3 ปีที่แล้ว

      Yes, from memory, the U he uses @8:30 is potential energy, which is usually capital U. Initial velocity is usually lowercase u.

  • @samarthsai9530
    @samarthsai9530 7 ปีที่แล้ว +1

    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

    • @tiscojack
      @tiscojack 5 ปีที่แล้ว

      Samarth Sai *necroposting* No it wasn't, he literally took it from the gravitational potential

  • @IAmNomadical
    @IAmNomadical 11 ปีที่แล้ว

    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..

  • @michaelgeinopolos6911
    @michaelgeinopolos6911 5 ปีที่แล้ว

    Can you just add two integrals (from a to b + b to c) to get action?

  • @LarghettoCantabile
    @LarghettoCantabile 6 หลายเดือนก่อน

    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.

  • @kigormley
    @kigormley 5 ปีที่แล้ว

    What a fantastic tutorial. Thanks a lot.

  • @justpaulo
    @justpaulo 10 ปีที่แล้ว +1

    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.

    • @Capuccinoish
      @Capuccinoish 9 ปีที่แล้ว

      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)

    • @justpaulo
      @justpaulo 9 ปีที่แล้ว

      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...

    • @Capuccinoish
      @Capuccinoish 9 ปีที่แล้ว +1

      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!

  • @LaureanoLuna
    @LaureanoLuna 8 ปีที่แล้ว

    It always confuses me when left- and right-hand-side don't match in dimension: 21:17, bottom.

  • @trentvaughn687
    @trentvaughn687 11 ปีที่แล้ว +1

    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

  • @Allthingstech3108
    @Allthingstech3108 5 ปีที่แล้ว

    You are an amazing teacher.Please suggest a introductory text book.I tried Goldstein it's too heavy.Thanks for the video.

  • @florirbiral4970
    @florirbiral4970 11 ปีที่แล้ว

    simply great as usual!

  • @menot5039
    @menot5039 4 ปีที่แล้ว

    that was cool. thanks from Morocco

  • @fantasticmrbond
    @fantasticmrbond 11 ปีที่แล้ว

    Excellent excellent overview!

  • @moritzalshuth7239
    @moritzalshuth7239 8 ปีที่แล้ว

    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...

  • @NoActuallyGo-KCUF-Yourself
    @NoActuallyGo-KCUF-Yourself 4 ปีที่แล้ว

    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?

  • @aisha.s614
    @aisha.s614 5 ปีที่แล้ว

    *this is an amazing explanation*

  • @chriscross1152
    @chriscross1152 11 ปีที่แล้ว

    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.

  • @ian-haggerty
    @ian-haggerty 4 ปีที่แล้ว

    The dL/dV terms should have a factor of 1/epsilon by the chain rule. This gives the time derivative inside the larger bracket.

    • @ian-haggerty
      @ian-haggerty 4 ปีที่แล้ว

      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).

  • @pSL-oy5gl
    @pSL-oy5gl 10 ปีที่แล้ว +2

    A Great video.

  • @iam774526
    @iam774526 9 ปีที่แล้ว

    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?

    • @irjensen
      @irjensen 9 ปีที่แล้ว

      +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.

  • @yanaungmoe6294
    @yanaungmoe6294 6 ปีที่แล้ว

    I worship you.

  • @CCPlaetean
    @CCPlaetean 11 ปีที่แล้ว

    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!

  • @cilva7able
    @cilva7able 7 ปีที่แล้ว

    Can anybody explain to me the difference between "Physics: Classical Mechanics" and Engineering: Dynamics"?

  • @مريممراد-ف3ث
    @مريممراد-ف3ث 8 ปีที่แล้ว

    Bravo Sir , If you expained some examples to simplified that concepts !

  • @chriscross1152
    @chriscross1152 11 ปีที่แล้ว

    At 24.53, the way you calculate dA/dx b is very particular, could you make it clearer ?

  • @raminnikzad6317
    @raminnikzad6317 11 ปีที่แล้ว

    Can i ask a question? : At around the 22':30" time why you didn't write A= L(Xa) + L (Xb) + L (Xc)?

  • @habblebabble70
    @habblebabble70 11 ปีที่แล้ว

    Well done DrPhysicsA

  • @LaureanoLuna
    @LaureanoLuna 7 ปีที่แล้ว

    Very helpful. Thanks.

  • @Cosmalano
    @Cosmalano 9 ปีที่แล้ว +2

    Analytical mechanics makes me feel like I'm on a hot date.

  • @AhmedMahmoud-lu1oq
    @AhmedMahmoud-lu1oq 4 ปีที่แล้ว

    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

  • @Yllemanden
    @Yllemanden 10 ปีที่แล้ว

    Great video ! Really informative.
    But it would be so much better if it was at least 720p... Really a shame. But nonetheless, great video.

    • @DrPhysicsA
      @DrPhysicsA  10 ปีที่แล้ว +2

      Thanks. I choose the resolution mainly based on the Time it takes to upload the video.

  • @quantumbro827
    @quantumbro827 ปีที่แล้ว +1

    I am very, very bad at memorizing, so l could just theoretically imagine it

    • @imex469
      @imex469 ปีที่แล้ว

      me too )

  • @canadasolarandacademics1759
    @canadasolarandacademics1759 4 ปีที่แล้ว

    thanks so much I am grateful

  • @peoplezk1
    @peoplezk1 11 ปีที่แล้ว

    As it tends to zero is different then being zero. He is talking about the derivative rather than the actual = to 0.

  • @rayhangu8403
    @rayhangu8403 3 ปีที่แล้ว

    sir can you make video about this with problem example solution?

  • @orsoncart802
    @orsoncart802 3 ปีที่แล้ว

    11:15 Typo: F = -(d/dx)mgx
    Minus sign was missing.

  • @SkanderTALEBHACINE
    @SkanderTALEBHACINE 10 ปีที่แล้ว

    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

    • @DrPhysicsA
      @DrPhysicsA  10 ปีที่แล้ว

      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).

  • @zamzamali4842
    @zamzamali4842 7 ปีที่แล้ว +1

    Thank you!

  • @RbtV92
    @RbtV92 11 ปีที่แล้ว

    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).

  • @user-ho9zb8hh6h
    @user-ho9zb8hh6h 11 ปีที่แล้ว

    hi Dr has also video subjects conservation laws, central force ...
    Have continued?? This will help me a lot
    Thanks

  • @GabrielSavageMusic
    @GabrielSavageMusic 10 ปีที่แล้ว

    At around 11:20 , shouldn't F = -mg ?

    • @DrPhysicsA
      @DrPhysicsA  10 ปีที่แล้ว

      Yes. Altho I was only calculating magnitudes. Generally PE is negative so F is positive.

    • @GabrielSavageMusic
      @GabrielSavageMusic 10 ปีที่แล้ว

      Got it, thanks for clarifying. :)

    • @ernestschoenmakers8181
      @ernestschoenmakers8181 9 ปีที่แล้ว

      DrPhysicsA But why is L = T - U, can this be derived from D'Alembert's principle?