In my first year in physics 1 course, my teacher tried to give an overview on Lagrangian Mechanics, but he used a lot math tools that i didn't know at the time, for exemple a Taylor Series with two variables. So, I don't need to say that i didn't get anything that he said. But your video can give a very good overview of Lagrangian for a first year!. Good Job! I want a Series!

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

@suddhasattasaha4793

2 жыл бұрын

Hey, if you want a complete course on Lagrangian Mechanics ( with problem solving sessions) , then here I am sharing a playlist with you, I created this series of videos to introduce LAGRANGIAN mechanics in a simple and exciting way, yet retaining the rigour of the subject. Hope you enjoy it ! THIS IS THE LINK TO MY PLAYLIST : kzread.info/head/PLZumX0a4ZsO0MSJ5Qujht8TOxm-w5XbBf

Nice reintroduction to the Lagrangian - it's been 50 years since I played with this.

@rohitjha8626

3 жыл бұрын

Still beautiful! isn't it?

@richardrigling4906

3 жыл бұрын

@@rohitjha8626 Yep!

@richardrigling4906

3 жыл бұрын

As you were going through the derivation, i could hear my classical mechanics professor's voice. Ghost from 50 years ago. Fascinating - to quote a certain Vulcan

@randomdude9135

3 жыл бұрын

So u never used it in 50yrs??

@randomdude9135

3 жыл бұрын

What's the purpose of knowledge is u rnt gonna use it?

In french "kinetic energy" is "énergie cinétique". There is no "T" in that. But it could come from the word "travail" which means "work" in french.

@joaovitorjungblut5225

Жыл бұрын

of course there is a 't,' it is right there: cineTique

@HakingMC

Жыл бұрын

I thought it’s because T is before U, so they used T.

@CliffSedge-nu5fv

8 ай бұрын

Whenever I see T used for kinetic, I usually also see V for potential. In Newtonian physics, U is used for potential and K for kinetic. V is used for electric potential per unit charge (voltage), so I appreciate the U to avoid that confusion. I still prefer K for kinetic, as T is often used for time period or for tension, depending on context.

@cmmaslanka

8 ай бұрын

Exactly. Travail mécanique...

@Xaver_44

7 ай бұрын

I always assumed it came from the word for work in European languages, which mostly start with "T", because there is a theorem that states that the total work is equal to variation of kinetic energy

This is amazing man. I've always had a lot of problems with parametrization, and although that was not the core of the video you made me see it in a different way. Keep it up

Really cool! I'm planning on getting a Physics degree and this just keeps me motivated.

@bockminster7474

3 жыл бұрын

Don’t do it until covid is cured. Trust me I’m dying

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

@moldysnek

3 жыл бұрын

@@bockminster7474 glad to know I'm not alone xd

@nurfitriyanaazizah3408

3 жыл бұрын

just don't

@DrAtomics

3 жыл бұрын

@@bockminster7474 Facts man, me too... What year are you? (Senior coming into Fall semester for me). Things have been super tough during COVID

Your teaching levels of physics is very good and it makes me to listen to your teaching

Thank you so much for posting this! The explanation is super clear and very helpful for me to understand this topic which is entirely new to me!

Nice introduction to LM ... An important point which was overlooked is the way in which LM can incorporate generalized forces (which would appear as extra terms in the E-L equation). Such forces must be taken into account when some physical forces acting on the system are not conservative (and therefore not expressible via potential energy). Such forces also are especially convenient/useful for assessing relevant constraint forces.

After watching you video, I felt Lagrangian mechanics is a very smart way to do it. This feeling is like there is a house, front door is closed. Backdoor is opened but people don't know there has a back door in this house. When try to open the door and into the house, Newtonian mechanics try very hard use force to breaching the door, and Lagrangian mechanics just into the house from back door.

@user-lb1ib8rz4h

Жыл бұрын

maths and even problem solving in general is poking on all sides until you see some give. then poke there more, rinse, repeat. and if you see similarities to another house, then it makes things even easier ofc every problems has tools that make it easier or harder. but often, differentiation is much easier than integration, hence the Lagrangian comes in handy.

@dybydx31

Жыл бұрын

Absolutely right

@CliffSedge-nu5fv

8 ай бұрын

Or can use brute force computational physics and take all the nails and bolts out and lift off the roof.

This is such a great breakdown of what's going on. I'm in a 700 level mechanics course and this is pretty much on par with what we've been reading (Goldstein)

@kingplunger6033

8 ай бұрын

700 level ?

@ramsey55

7 ай бұрын

@@kingplunger6033grad school

should the y_double_dot on 10:37 be minus g because it is acting downwards or I am missing something

@Vaderphobia

3 жыл бұрын

You are right 👍🏽

@user_2793

3 жыл бұрын

Yep

@Jacked_R_Us

3 жыл бұрын

ye its -g

@remavas7076

2 жыл бұрын

He lost a minus when solving the last equation.

@piotrbiy8712

5 ай бұрын

I noticed this flaw too. Fortunately, someone had described this problem earlier, so my worries quickly disappeared.

Please keep making videos on Lagrangian mechanics 🙏

@DotPhysics

3 жыл бұрын

you know it.

simple and easy to understand, thank you!!!!

Came here from the subreddit Awesome video, liked and subscribed

This was a really good video, Physics is very interesting subject, although a little complicated.

@kamalenduhaldar5805

3 жыл бұрын

Every indian jee adv aspirant is kinda junior physicist lol... (me😭)

@knotoftime9680

Жыл бұрын

@@kamalenduhaldar5805 🗿

I wonder sometimes, how can something be explained this good. Thanksssss

@DotPhysics

2 жыл бұрын

Oh. That’s nice. Thanks!!

Extremely wonderful video 👏.

At 13:14, the derivative should be positive because you defined y as -l*cos(theta). Although it doesn't affect the result as you are squaring it later!

Exceptional introduction- THANK YOU

@quantummechanic8897

2 жыл бұрын

The best playlist kzread.info/dash/bejne/mouIkphyqsydnbA.html&ab_channel=BiPhysiMath-Special

This video is really helpful, but I think the diagram at 4:45 could use a redraw of sorts ;)

@DotPhysics

2 жыл бұрын

I finally get this comment. I feel stupid now.

How will we obtain the Lagragian for an object sliding under the influence of force 'F' on a frictional surface?

T can be calculated- using resolution of vectors resolute T in vectors components as Tcosx (theta=x) and Tsinx. Tcosx and mg gets neutralized and we are left with Tsinx. Since, bob is moving in circular trajectory it implies we can equate Tsinx= mR(dx/dt)^2 where R is radius Therefore,. T= mR(dx/dt)^2/sinx

Mr physics explained make more video on Lagrangian principle it's so helpful for me👍🏻

Thank you so much Sir for this wonderful video. I am starting this topic in my 1st year. It is very helpful .

@yansayidiyegrace854

2 жыл бұрын

Are You Physics Student at University? I recommend this: kzread.info/dash/bejne/mouIkphyqsydnbA.html

@quantummechanic8897

2 жыл бұрын

The best playlist kzread.info/dash/bejne/mouIkphyqsydnbA.html&ab_channel=BiPhysiMath-Special

It's been a long time since I studied multi variable calculus. Can you remind me why you can assume ydot doesn't depend on y? When taking the partial of ydot with respect to y my first thought is that ydot could possibly be equal to a function of y so I wouldn't assume the ydot term would be zero.

@bingusiswatching6335

2 жыл бұрын

I'm new to this but I think its more to do with the lagrangian itself, to predict an objects motion it requires an initial velocity and position which are not dependent on each other in configuration space?

@user-lb1ib8rz4h

Жыл бұрын

they're taking the partial of L wrt y, and L is a function y, ydot, and t. so we ignore the ydot and t if taking the partial wrt y

This video was really helpful!

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

Great video, helped a lot. Also, would you happen to know why we use T-U as the lagrangian? I can't seem to find a good answer anywhere

@gibbogle

8 ай бұрын

Same here. I'm guessing that was a lot of development by different mathematicians, maybe spanning years, to arrive at L = T - U. The teachers don't go into the history.

In your final solution for the pendulum problem you have upper case L in the denominator. It should be lower case.

Excellent straightforward explanation

@quantummechanic8897

2 жыл бұрын

The best playlist kzread.info/dash/bejne/mouIkphyqsydnbA.html&ab_channel=BiPhysiMath-Special

Thank u sir for this nice explanation 👍🏻👏🙏

Very good explanation !!

Thank you so much 😘 From vietnam with love

excellent teaching sir. But just one doubt, in potential energy, for Y we have to substitute (l - l cos(theta)) right??

11:57 The Potential energy is mglsin theta since the restoring force is mg sine theta

This is a really amazing video!. Actually I was a little bit confused in 13:11, why y' is d/dt(lcos(theta))? it shouldn't by d/dt(-lcos(theta))?

@NateRiver-ph9co

3 жыл бұрын

I´d like to know as well

@user13rs258

3 жыл бұрын

It gets fixed while adding their square if you have noticed it, even if it is fixed by mistake. 😂😂 I mean because of squaring and getting the right answer 😁

Great Videos keep it up!

At time stamp 10:30, shouldn't it be mg = -my dot?

Will it not be Theta double dot =- g sin Theta/ Lower case L rather than capital L in the denominator? Also del L/ Del theta dot is zero in the first term because Theta dot is a function of time and not Theta. Am I right?

For people that can't simply get over using the equation without knowing where did it come from (god knows I can't), video from Eugen Khutoryansky gives a rather satisfying explanation of Euler-Lagrange equation derivation.

@SolidSiren

Жыл бұрын

I can't let it go ever in any instance. I can't shutup and calculate. I need to know the derivation, and why, and how, and inside and out. How else will I fundamentally understand the things I'm doing?

@amirpasagic162

Жыл бұрын

@@SolidSiren I feel you brother. That is why I warmly recommend this one. Also 'Physics with Eliot' channel has amazing resources on this.

Good video and great explanation.

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

@dybydx31

Жыл бұрын

Great content

How does the problem change when you have a pendulum in 3D space? when I plug my z value in, is it also lcos(theta)(theta-dot)? Or would the angle be different when referring to z? And then how does that affect the rest of the process??

Great video and great explanation!!! I'm becoming a fan.

9:49 why 1st term with dy/dt or T in L when we do partial derivative of L it was ignored. dy/dt can have y in the equation in general and in fact in gravitational scenario it did. Wonder.

This might be a dumb question because I don't get the part from 12:20. I know that kinetic energy is (m*x*^2)/2 from newtonian mechanics but did you add an *y* because there is also the y coordinate? Or, if there would be an Oxyz space would we have to add also an *z* over there?

@DotPhysics

3 жыл бұрын

Since we are using a coordinate of theta for the motion, we need to get the kinetic energy in terms of theta. In general, that can be tough (yes, you could see it in polar coordinates). So, if we get an expression in terms of x and y (and z if you need it), then I know the kinetic energy is (1/2)m(x-dot^2+y-dot^2)

@leoliu7492

3 жыл бұрын

this is the velocity in 2D.

@100AngelBoy

3 жыл бұрын

@@DotPhysics I see, thank you! Dude, you are actually good 😁

i have some doubt why we take the derivitive of the lagrangian function for the solutions ? and how does it work ?

Great content, thanks ☺️

Could you explain why L is defined as T - U? Also when you were doing the partials around @10:00, even though y dot and y are different variables, isn't y dot still dependent on y and vice versa? So if you are doing the partial of one variable, wouldn't the other be affected as well, in other words when you are doing the partial of y the y dot is moving and vice versa so that the results are not clean? Help me if I am over thinking or there is something to this.

@maalikserebryakov

2 жыл бұрын

Thats like asking why is newtonian Force defined as the product of mass and acceleration. These are just definitions invented to make calculation possible. you can invent a new definition yourself but the difficult part is to come up with a definition that is useful in calculation

@classictutor

2 жыл бұрын

@@maalikserebryakov Useful for calculation is good enough for me. I thought there was something more deeper.

@maalikserebryakov

2 жыл бұрын

@@classictutor yes thats all there is to it nothing deeper at all 👍

@MrSidney9

Жыл бұрын

@@maalikserebryakov Net force being equal mass times acceleration is not “a definition invented “ it’s a fact about the natural world transcribed in mathematical term. L=T-U is however purely definitional, and useless considered by itself; However, the Lagrangian EQUATION, is a statement about the physical world.

GOOD JOB with this movie... Now I will check with others u movies. Maybe this channel is worth to recommend to others. :-)

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

nicely explained !

I like the introduction series

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

then what should be the equation on the motion of the ball?

Thanks for the super tutorial! (Last formular of the pendulum: instead of "L" should be "l" [length of pendulum])

Great one !!!

So simply explained thanks ❤️

@DotPhysics

Жыл бұрын

Glad it was helpful!

AMAZING ! , SUSCRIBED INMEDIATLY

i love this channel

Amazing intro to lagrangian.

@DotPhysics

Жыл бұрын

thanks!

Not sure about the right hand plot at 5:39. S, as defined by the integral, is a just a constant for each path, since y is a function of t, and we are integrating wrt t. So any plot S should be against "path". How is that represented by the horizontal axis?

@miloszforman6270

Жыл бұрын

Sorry to say that, but it's an awkward BS diagram as well as an awkward BS explanation. Thumbs down.

Great lecture!! Thanks

@DotPhysics

9 ай бұрын

Glad it was helpful!

thanks for a great video!

@DotPhysics

6 ай бұрын

Glad you liked it!

At 17:19. Shouldn't it be -(g/l)*sin(theta) ... lower l as capital L is used as the Lagrangian?

Great vid!

I just realized how important is this when I saw the "LAGRANGIAN" is so big. !

This video deserves to be prefaced with links to the sources for related and assumed knowledge, so people can get the pre-requisite knowledge required to understand and appreciate this video.

I can see this is a BIG DEAL!

This is great! Thank you! Does someone learn this as an engineer? Because I study Civil but have never seen this.

@DotPhysics

3 жыл бұрын

For civil engineering - you might not get to this stuff.

@diatlemaboe9942

3 жыл бұрын

Mechanical engineering - vibration, yeah

@nicolassanchez7259

3 жыл бұрын

@@diatlemaboe9942 yess I'm taking a class in vibrations and you see this stuff

Should that derivative with respect y be my' * mdy'/dy - mg?

Thank you! Thank you!

Afte practising so many questions, I have seen making mistakes due to writing x prime or x dot to show the velocity in x direction and it's not so efficient to always write like those old books, I do not make mistakes in differentiation or calculus, I make mistakes in distinguishing between velocity and coordinate. So I start writing Vx or Vy or Vz or Vi to show velocity XD

Awesome video 😍

@DotPhysics

3 жыл бұрын

Thanks 🤗

T was chosen by the person who introduced the concept of kinetic energy. It stands for "translational" cause it's the energy of movement

Wow, u made it easier

Great! Where does it come from?

12:05 Potential energy is not - mgl cos@ but mgl (1 - cos@)

Thanks bro cool vid

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐

Aahh yeah this man needs more than just one like

Hi, Dot physics I have two question and im seeking my answer for long time never satisfied with any.1) why lagrangian are defined like L=T-U??? Why not any otjer form like L= sin T- log U or amy othe rkind of weired combination??? Dpes lagrange derrive this perticuler form from Anywhere or he got it in his dream??? 2) if a system is in motion with non conservative force, only like friction can we still define Lagrangian??? How???

Thank you so much ❤

What courses in mathematics do I have to have in my body before going inside the famous Lagrangian? Somebody can explain?

@DotPhysics

2 жыл бұрын

Really, you just need derivatives and partial derivatives. So, you would probably be fine with something like Calc II

Very clear explanation of how to do problems using lagrangian dynamics, but I still wonder where it comes from. Why did someone define L=T-U in the first place, etc. Great video!

@DotPhysics

Жыл бұрын

I think, like many concepts in physics, we use the Lagrangian just because it works. Lagrange showed that if you defined L, then the action integral would be the same as the actual trajectory. It's crazy.

@miloszforman6270

Жыл бұрын

_"Great video!"_ _"but I still wonder where it comes from"_ Isn't that some kind of contradiction? If you can't understand it from the video, probably it's a bad video. We would not have to bother, but this guy is stealing our time.

Thank you so much

Wym there is no tension equation? T = mv^2/r + mgcosx

Great explanation! I was trying to go through the code, and it generates just one of the two plots. Any chance you can post a link to the entire code with the two plots?

@DotPhysics

2 жыл бұрын

Let me go look at the code. Hopefully, I can give an update soon.

@DotPhysics

2 жыл бұрын

are you talking about the two graphs - world plot vs. action plot? If so, I recommend this super awesome site - www.cleonis.nl/physics/phys256/least_action.php

I don't think the T has a particular meaning in french either...

Anyone can tell me the playlist? I want to watch the other examples. Thanks!

@DotPhysics

2 жыл бұрын

Here you go - kzread.info/head/PLWFlMBumSLSbX-yG0eUl5hBa_I6Oz5k7B

@michaelli8523

2 жыл бұрын

@@DotPhysics Awesome, thank you for the excellent series!

Could someone explain to me why the Lagrangian is conceptually defined as L=T-V? I am learning and I would be very grateful if you could answer this doubt about my concept. have a good morning, afternoon or evening

@asprinon3146

8 ай бұрын

When lagrange derived euler-lagrange equations from de alembert's principle, it was found out that...the T-V is which comes in the equation...and he named it the lagrangian So we say L=T-V

T stands for travaille i think. Which means work

at 11:58 shouldn't the potential energy be U = mg(l - lcos(theta))

@st_s3lios860

3 жыл бұрын

It's actually the same. You just put the origine of potentiel to the bottom when he put it to the top. But whatever, the constant will diseapper when you will derive (sorry for my bad english)

@atheroot

2 жыл бұрын

@@st_s3lios860 no, it's not the same. Looks like the author don't understand the topic.

Amazing

Can proof that Newton laws are equal to Euler Lagrange equation

Nice Explanation

@yansayidiyegrace854

2 жыл бұрын

Are You Physics Student at University? I recommend this: kzread.info/dash/bejne/mouIkphyqsydnbA.html

@quantummechanic8897

2 жыл бұрын

The best playlist kzread.info/dash/bejne/mouIkphyqsydnbA.html&ab_channel=BiPhysiMath-Special

@ 10:36 its negative g. great video!

i prefer bance newtons cradle at each instance practice problem sets never tried double pendulum other than upside down newtons cradle at inverse forces

that path from 4:47 is something familiar !?

Perfect

Mewton: force LaGrange: energy

what is the difference between Lagrangian mechanics and Hamiltonian ?

@DotPhysics

2 жыл бұрын

This might help - but it doesn't fully answer your question. Here is the problem of a block sliding down an inclined plane. I solve it three ways: Newtonian, Lagrangian and then Hamiltonian. kzread.info/dash/bejne/f36m0LeHp6jLZMo.html

Kinetic energy translates to "énergie cinétique" in french, so the T probably doesn't come from there ^^

At 9:35 you say that the kinetic energy does not depend on y. Surely from a physics point of view the kinetic energy is a maximum at the bottom, falls to zero at the top of the curve, then increases again on the way down - so it is continuously changing with y. I am confused.

@mihadbinislamtanim6267

3 жыл бұрын

The kinetic energy depends on the 'derivative of y' not y. At the bottom the y is 0 and it's derivative is at maximum, so kinetic energy is at maximum. At the maximum height y= max but it's derivative is zero, so there's no kinetic energy there. So kinetic energy is changing with derivative of y and not y

@learnerman5712

3 жыл бұрын

@@mihadbinislamtanim6267 But could not derivative of y itself be expressed in terms of y so that one could say that kinetic energy is indirectly a function of y?

@fargle2008

3 жыл бұрын

@@mihadbinislamtanim6267 Thank-you for taking the time to answer my question. You say "At the bottom the y is 0 . . . kinetic energy is at maximum". Then you say " height y= max . . . so there's no kinetic energy there [ i.e. KE = 0 ]". So you are repeating my assertion that KE does vary with y. The total energy is the sum KE plus PE. As PE increases linearly with y. KE must decrease linearly with y to keep the total energy constant.

@mihadbinislamtanim6267

3 жыл бұрын

@@fargle2008 Thank you for taking your time to point out my mistakes. Your right that kinetic energy does vary with y. But what I wanted to imply was that the kinetic energy term was depended on the value of y• and not y. Meter's and meter's per second aren't same. If we take the Taylor expansion and work for y• we will find a function which is dependent on y. I just wanted to be generic with the dimensions of the function. Sorry if my first comment was misleading 😅.

@mohammaditani4558

2 жыл бұрын

It's a partial derivative with respect to y_dot that's why it doesn't depend on y. I don't think he meant the kinetic energy doesn't depend on y.

Thank u sir.