Projectile Motion Using Lagrangians lolwut

[@semiawesomatic6064]

That's the biggest overkill ever. That's like nuking your house to kill a fly.

[@chymoney1]

semi awesomatic that’s how kinematic is derived dawg

[@semiawesomatic6064]

chymoney1 I always thought It was used by starting with newton's second law. Meh.

[@Bignic2008]

It's like using Fermat's Last Theorem to show that the nth root of 2 is irrational for n > 2.

[@welcomeblack]

You can nuke it even more by showing that x->x+delta or y -> y+delta is a symmetry of the action and deriving the corresponding conserved quantities using Noether's theorem.

[@MarkMcDaniel]

Agreed. Basic kinematics would've been remarkably easier.

[@GeodesicBruh]

Using Lagrangian equation on this is like fighting your high school bully’s son

[@comradepeter87]

LOLL why is this so accurate? XD

[@HackersSun]

8I I'd b slap him anyday

[@yash1152]

i have seen u at other places here on youtube too. hi lol

[@katgirl3000]

:D Hilarious!

[@johnespino886]

This was actually given as a homework for us in integral calculus/differential equations and while it may seem overkill it really helps you see how we arrive at the formalism, and how it can be used in many simpler maths

[@remy7541]

When you want to flex on newton

[@user-en5vj6vr2u]

When you forget which kinematic equation to use

[@abdusabdud8218]

Yes but is this very necessary?

[@lPlanetarizado]

@@user-en5vj6vr2u this lol

[@maxwellsequation4887]

And Newton comes back to life and discovers 4 new branches of mathematics and winks at you

[@bringbackthedislikecount6767]

Virgin Newton vs Chad Lagrange

[@RDash]

That was interesting, can you please do the hamiltonian next?

[@chronicsnail6675]

@Diego Alonso I'm not glad... Shameful

[@electricbill4884]

Hey Andrew, I don't know if you'll ever see this, but I just wanted to say thank you so much for making this video! I studied mechanical engineering in college, and when we started lagrangians in our dynamics class in third year we just jumped right into spring mass damper systems, without developing any real intuition. I think the closest we got to a proper explanation of what we were doing was an abridged derivation in the notes for the euler-lagrange equation lol. Anyway, I had been meaning to return to this video for years, suspecting it would help with connecting the dots between newtonian mechanics and lagrangian mechanics, and my only regret is that I didn't see this sooner! I think if I had seen this back then I would have grasped the examples a lot sooner, and without as much heartache. I think it should be best practise in any class making use of this technique to return to a simple case such as the one in your video. Thanks again man!

[@beautifulmath5361]

Very clearly explained, both at the level of equations and deriviates, but also at the general level in explaining why we're doing this and how it fits into the larger picture.

[@XxS4NN4SxX]

Could you make a video applying this to a more complicated situation? I understood this process, but it would be nice what would change in a different problem like, for instance, a pendulum. Nice video!

[@Tomaplen]

or maybe YOU could do it? :D

[@Erik20766]

JSG you literally just plug in the Lagrangian into the Lagrange equation of every generalized coordinate and get a set of differential equations.

[@katgirl3000]

Even though the Lagrangian for a simple example is overkill this would be a very clear way to introduce people who just learned about the Lagrangian/Euler-Lagrange to its different nomenclature compared to 1st year Newtonian mechanics. Pretty nice! Now I gotta find the Hamiltonian video! :)

[@jacobharris5894]

I remember seeing this video a couple years ago but I finally got introduced to the Lagrangians the first time in my Astrophysics class. So I had to come back and watch this video again, because I love how you explain things.

[@philippjohannsen6217]

Much good. Thank you for this video! A couple of weeks ago, I started studying Classical Mechanics on my own because of vacation, and I'm almost done with all the stuff that was covered in University Physics, so the next thing that I have to look at is Calculus of Variations and Lagrangian Mechanics. The last two videos showed me what to expect, and I'm so excited to learn more about it!

[@osirisapex7483]

Philipp Johannsen for calculus of variations I recommend the online Feynman lecture “The Principle of Least Action.”

[@philippjohannsen6217]

Osir isrex Thank you, I will definitely look into it :)

[@freebiehughes9615]

You are studying these things on your own and doing it easily! You are a beast, my friend! Beast is a form of high praise, btw!(just in case English is not your native tongue!) How are the studies going 3 years later? I am only at the General Physics and Calc I stage, myself, so these videos show me that I have a lot to learn.

[@Mikebigmike94]

@@freebiehughes9615 are you also a self studyier if that’s a word 🤣 do you self study i mean. How’s it going?

[@fosheimdet]

I love this. Like you, I've come to the conclusion that Newtonian formalism is for noobs and campers.

[@loganfisher3138]

Now account for the curvature of spacetime near the surface of Earth.

[@meofamily4]

Strangely satisfying. Like having a cold beer after working out in the yard all afternoon on a hot day.

[@drokrath]

I watched this when it came out and I was completely lost but now I came back to watch it again and I got bored because I already knew how to do it. Strange how much you can learn and change in such a short time.

[@akankshasingh5749]

Thanks so much for this awesome video!!!Loved it!!!!Overkill or not,this is exactly how I was taught to use Langrange equation!!So deriving the equations of motion was the very first thing we did using Langrange equation,so I loved it!!!Applying this equation in simple cases really helped me get the hang of it.

[@pipertripp]

Would LOOOOOVE to see the Hamiltonian version of this next. Then some more complex examples of each would be mint, mate. Really appreciate the time you take to bash these out. They're fun to watch and give me some sense of what's out there to explore.

[@JaxzanProditor]

I would love to see the Hamiltonian! I came out of this video only slightly confused, so I think on the whole this was pretty great

[@Barfriedrich12]

Next time the projectile accelerates downward in g(t) corresponding to his height. And everything is relativistic.

[@insouciantFox]

this is clearly what Lagrange had in mind.

[@sherlock_norris]

short sidenote: if you want to calculate a problem with friction (that generally has no potential) you would have to add a generalized form of your force of friction on the right side of the equation (direction depending on the generalized variables you are using).

[@johncrwarner]

Using the Lagrangian approach to get to these simple kinematic equations was very useful (it was overkill but if it is equivalent you should get the same results) - I have actually never done a Lagrangian on a simple system that even Galileo, the last scientist to tackle this pre-calculus, could solve without calculus.

[@erockromulan9329]

I followed all of this. I need to go to grad school. Nice job!

[@Subscribifyable]

I would love to see a derivation of the Hamiltonian. It would be great if you could explain what the point of the Legendre transform is; the resources I've been looking at have not focused on the physical intuition of it. Thanks for the videos!

[@davidfenoll2332]

Next time for double pendulum please!

[@abdusabdud8218]

Solve it with the help of newtonian

[@nicoferreira4370]

@@abdusabdud8218 Satan, pls chill.

[@marinecwo4]

Good video for enhancing understanding of the kinematic equations.

[@drandrewsanchez]

So cool! Can we see an example of a complicated system, such as with friction, or the double pendulum you keep mentioning?

[@Lifefinder15]

loVe you sir from pakistan there is no teacher like yOu on youtube gReat great

[@sushmatripathi1341]

While doing partial derivative of kinetic energy in wrt y why we not consider that v in y ( y single dot) is itself a function of y coordinate.

[@yash1152]

5:33 so, del y / del y . = 0 ?? i have just barely touched the partial derivatives, so, am getting a bit confused

[@superspeedstergaming20]

Amazing man so cool wanna see an application of lagrangian on Double pendulum

[@CraftCrazy69]

Why is v^2 turned into (xdot^2 + ydot^2) when put in the langrang?

[@christianndjanda5834]

At 4:09 why is it y dot squared? I thought that x dot squared was enough because it is velocity is the derivative of position with respect to time

[@alexanderrobertson5530]

Christian Ndjanda y dot is squared because it is the kinetic energy in the y direction. Since kinetic energy is 1/2mv^2 the kinetic energy will be 1/2mx'^2 + 1/2my'^2. Velocity is a vector, therefore you can resolve it into its components x, y, and maybe z depending on the problem. Most problems in classical mechanics will be 2D so we usually only resolve it in 2 dimensions because we pick a coirdinate system where the motion is in 2D. He just factored out the 1/2m from the two terms.

[@theflaggeddragon9472]

This should be a series; if you derive the Euler-Lagrange equation from Least action and do a whole bunch of calculations in the 3 formalisms, then eventually just use Lagrangian and Hamiltonian because F=ma is hopelessly unwieldy!

[@hendrycaven]

Andrew you look hella ripped. When do you have time for gym?

[@chrisallen9509]

Prometheus he benches 3 plates so

[@3117master]

I bench 4....pounds 😊

[@chrisallen9509]

at what bodyweight?

[@abdusabdud8218]

@@chrisallen9509 m= about 77 kg ×value of g in America

[@federicopagano6590]

I loved this video. I have a question U used euler lagrangian equation because 1)u are calculating any stationary points of the lagrangian? ....or 2)u used the euler lagrangian derivative formula because the lagrangian is constant so it's derivative with respect to time is zero? 3)is really the lagrangian a constant value like the mechanical energy ? Because there is a minus instead of a plus. Is the value "L" constant ? With this minus in the middle?

[@mattias2576]

So weird, when i first watched this video two years ago or so, i had no idea what he was doing, but now in my 3. semester of undergrad physics, i at least understand the math a bit

[@Amoeba_Podre]

Yea it seems so complicated once you first see it but its really simple once you know the notation. Just learned about this yesterday from drphysicsA

[@sushruttadwalkar7701]

This somehow helped me solve a problem i was stuck on LMAO; also love your vids.

[@brandonberisford]

Holy shit this is so well timed, I just finished self studying the air resistance projectile motion problems. Do using the langrangian or hamiltonian fomulations simplify projectile motion with air resistance greatly? Because holy hell, its a nightmare with newtons laws.

[@Sorvah]

Yes. Why would we not want you to show us this problem using the hamiltonian?

[@JamFilledDonut]

Perhaps a brief look at the Hamiltonian version would be good but I'd like to see where Hamiltonians come in at their most useful

[@HackersSun]

You're right It is necessary Like seeing how it works If we're in the field we're going to have to do something similar to this but not specific?

[@quantumdothunter]

g is not positive. It is in the negative y direction. In the final integration for dy the sign gets flipped and one ends up with the right equation, i.e. Viy-1/2gt^2

[@lPlanetarizado]

do you know about the lagrangian in a elastic solid? I know the idea is the same, but I have a hard time understanding

[@jdarcy5714]

with mass = 1 kilogram and an launched at an angle with some initial velocity, does the Lagrangian produce : y(x) = [(tan(ø)] x - [g/2v02 (cos2ø)] x2

[@avinashmohapatra9355]

Like it really helped me now I can try to figure out some equations using lagrangian formalism

[@Blackmuhahah]

you could do the same in polar coordinates, just to show the "generalized coordinate" part of the EL-equations

[@alexanderyayne2838]

the dab at the end lmao

[@michalbotor]

is the trajectory of the projectile a geodesic? and if so, is it always the case that for the free motion (i.e. motion without constraints) the solution is the geodesic? if i were to be projectilled, would i feel weightless?

[@nitant5472]

Lol did this 3 months ago it feel nice to listen the lecture which I know

[@OliverBatchelor]

Nice, I know very little beyond highschool physics - but occasionally I run into little bits and pieces and it makes no sense, at least I can follow what you're doing.

[@abdusabdud8218]

Please make a video on calculus of variation

[@martinscaune4165]

In last integration you forgot +c that would be initial y coordinate. How do we integrate friction that is proportional to v^2 in these equations. Is it even possible to get these equations with friction inside?

[@martinscaune4165]

Can I get equation of the path with the friction? I guess it wouldn't be a parabola.

[@theflaggeddragon9472]

Can you derive the Euler-Lagrange equation from the principle of least action for us?

[@Scaryfast543]

You deserve more subs. Keep up the good content!

[@Tomaplen]

Can you solve it with general relativity?

[@vinayakhotkar4593]

ask him to solve using permutations lol

[@israelantezanalopez7267]

Usefuln't thx for sharing

[@nurbeksaidnassim7990]

Hamiltonians and also could you show Lagrangian used for solving a problem of a body sliding on a moving inclined plane (plane moves as well)?👌

[@spencertaylor6910]

Awesome video! Thanks Andrew

[@okultarastirmaci]

Can you make it with air resistance? Using Lang.

[@simonsteiner4743]

i appreciate it bro i feel THE POWER OF OG Lagrangian!

[@debunkthis]

Sort of random question but in quantum field theory is it valid to think of a Hamiltonian or does one only look at Lorentz invariant quantities

[@AndrewDotsonvideos]

You're right that it's helpful to look at lorentz invariant quantities, but the hamiltonian (density) is still the 00 component of the energy momentum tensor which is useful. It's also still required when looking at different pictures (interaction, heisenberg, etc). And finally, you actually derive the Feynman path integral by considering matrix elements of the time evolution operator, which is in terms of the hamiltonian.

[@johnsalkeld1088]

Then you should change it to be a large sphere with surface gravity level of mgh with 2 d polar co-ords and finally use the gravitational potential on the same large sphere - it could be used as an introduction to concepts around perturbation early on

[@amandeep9930]

Do the one for spinning tops

[@josedecabo1]

thats a big wrench u got there friend

[@user_2793]

I don't understand how the Lagrangian formalism is completely equivalent to Newton's. Isn't it stronger?

[@abdusabdud8218]

Hey Andrew I am a high school guy ,I can't understand ,what's the need of lagrangian and Hamiltonian mechanics we can solve mechanics problem without of it, it's also a difficult method , so what's the need of it

[@CoreNexusGaming]

hamiltonian in a qm problem?

[@DavidSousaP]

That was awesome. Hey, can you do it for a slide plan? That would be great. And to be honest I thought that was easier than with Newtonian mechanics. There you can easily make a mistake with vectors or such. I don't know. I do that.... Great video, dude! You're as cute as ever! ❤

[@namechane1758]

is that a odu hat?

[@ariusmaximilian8291]

Plz do a harder one with hamiltonian Love ur videos

[@extraordinaryhuman1806]

Thanks. I like to start slow

[@Tomaplen]

Can you solve it with Hamilton-Jacobi?

[@tatjanagobold2810]

It is as if you knew what I am currently studying, because I am studying Lagrangian Mechanics at the Moment :D is the lagrange formalism not best used when there are constraints? That is how I understand it

[@dox1755]

Hey bro i really wonder how to calculate the arcdistance of the projectile motion ? Is there any way to do it ?

[@chrisallen9509]

What the guy above me said is right, but more generally, just parametrize the curve then take a line integral of it. Or use the calc 2 method which is the integral of 1+f’(x)^2 dx over your bounds

[@dox1755]

Chris Allen bro in general its hard to find a function for an any given curve i thing the first answer makes more sense in general cases

[@chrisallen9509]

yeah true, arclength is easier this way. Still can't hurt to know another method tho

[@dox1755]

Chris Allen yeah true is one but the ways of getting it is dozens

[@zoltankurti]

Chris Allen sqrt(1+f'(x)^2) is what you have to integrate.

[@NamaSaya-wg9gn]

Why y component of velocity including in kinetic energy?

[@bruhmoment1835]

Kinetic energy is treated as a scalar.

[@lucagirelli5223]

super cool please do hamiltonian 💯

[@edmundwoolliams1240]

Next, do it using the Hamilton-Jacobi equation! :p

[@poutineausyropderable7108]

This video thought me what a lagrandian was. *Edit: even though i didn't know what a lagrangian was, i kinda used something similar to try to solve problem in the past that i learned by myself/found on the internet under another name*. I'm a first sessions college student(We started derriavtive) even tough i did calc 1 2, 80% of calc 3. 80% of differential equation. A little bit of linear algebra. A little bit of partial differential equation. (I'm 17). Could you use that to do a Simulation of an asteroid entering the solar system? You set the coordinate of the sun at 0. You say its L=(0.5m(y.^2+x.^2)-GM1m/sqrt(x^2+y^2)-(Potential energy of what happen if you fall through the sun to its core). Which is the integral of (Gm/x^2 * 4pix^3/3*Rho(x)dx from 0 to the radius of the run). Also, tried it. Brougt me back to where i was before. A system of differential equation.

[@Tomaplen]

Definitely you can. You only need the equations of motion of the objects

[@coffeeguy.3438]

Try Hamilton's 2n equations next.

[@coldmash]

nice video more of that pls! next time tacle a harder problem

[@bavid4430]

you can tell hes been using lagrangian mechanics too much when he writes his a's like curly d's lol

[@norielsylvire4097]

You forgot to add a constant C (that when t=0, will be the initial Y coordinate)

[@music2am117]

Thank you brother

[@sebasaman]

Hamiltonian version pls

[@TurdFurgeson571]

It was hard to follow this without the marker constantly fading like they do in a real physics lecture.

[@edrodriguez5116]

How old are u bro?

[@vtrandal]

Hey you misspelled something. I’m not sure what. The tears are flowing. I’m so wounded. In protest I’m chewing the same piece of gum for a month.

[@chrisallen9509]

Isn’t the fundamental basis of your equations still incorrect in a more general case? All projectile motion is based off of constant acceleration downward, but this clearly isn’t the case as shown in Newton’s universal law of gravitation. The acceleration and force both follow an inverse square that is radically dependent. To be more accurate shouldn’t you have used 1/2mv^2-GMm/r? This might be a trickier differential equation to solve lol. And I guess on the basis of being “most right” you should really have used relativistic kinetic energy and relativistic gravitational potential. But that would be even more overkill...I’d still be interested in seeing a video on how to solve these more complex differential equations.

[@zoltankurti]

Chris Allen in special relativity the lagrangian is different from the classical one. So you not only have to include relativistic terms, but also have to think about what the lagrangian should be. And if you use the inverse square law for the force in the classical case, you get the motion of planets.

[@unknown360ful]

0:35 What do you do Andrew? Drink and know things??

[@AnuragXorma]

unknown360ful he is a secret Targaryen

[@paulstansell3697]

Fuck I love this channel :D

[@ISapTout]

Video idea Could you go over this segment (from 2:11:10 to 2:16:00) of Joe Rogans podcast with Sean Caroll and explain the mathematics behind what Sean's saying. LINK -> kzbin.info/www/bejne/kKXbq4CYbqijiq8 For example at 2:12:00 he talks about people doing a calculation on radiation and getting infinite solutions, and goes onto say that plank treated it like there were particles involved and it fixed it. Frist off what was the original equation/values that yielded infinite solutions and what did plank do to fix it??? Then again at around 2:14:30 he mentions a calculation about evaporating atoms and bohrs fix. What was the original problem (mathematically) and how did Bohr fix it? I'm not sure how you would make a video like this. Just that you're my go-to physics guy.

[@ISapTout]

Also Id recommend watching the whole podcast and also Sean's podcast Mindscape (more specifically episode 2 with Carlo Rovelli).

[@Asdun77]

god bless you .

[@monsieur910]

Damn this was clear!! Thanks!

[@georgetait386]

Watching this I cannot wait to start my physics degree

[@drandrewsanchez]

OMG 0:01 I just realized how funny it is you're pointing at nothing

[@AngelMartinez-vg1nz]

Use Hamilton !!! Also work our another problem plzzz

[@algonte]

Hamiltonian PLEASE

[@quahntasy]

lolwut

[@resident5124]

sweet dab. sweeter video.