MIT 2.003SC Engineering Dynamics, Fall 2011 View the complete course: ocw.mit.edu/2-003SCF11 Instructor: J. Kim Vandiver License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
Indeed! And for students with profs whose first language is not English, it really helps until the student's ear acclimates to the prof's accent if he/she is difficult to understand.
I'm studying mechanical engineering in Italy, our professor's introduced the Lagrange equations to us making tons of calculations and partial derivatives without even explaining the sense of what he was doing. This, however, is by far the clearest explanation I've found about this fascinating topic, I wish I would have had a professor like him teaching my courses.
exactly. I'm from Pakistan, a country that is much father than even Italy. all we did is become better calculators. never learned when these concepts will come to use or even what the equations mean, how we can use them.
I really appreciate the open courses from MIT. They honestly saved my life. Much more intuition instead of plain math formula are taught in the videos than in the lectures from my college.
This is the most insightful and detailed lecture on Lagrangian Mechanics out there. Thanks J. Kim Vandiver. Your problem solving approach is so stimulating and engaging!
Genuine interest of a brilliant engineer for teaching. The best explanation of the Lagrange equation showing the way to solve hard problems. Now I know MIT’s reputation.
Professor Vandiver, thank you for an incredible lecture on the Introduction to Lagrange Equations with detailed Examples. This lecture really explained Lagrange Equations in full detail.
@@lauraesthela6941 I personally think that lectures should be spent more on example problems instead of rigorous proofs and derivations. The lectures are primarily supposed to be a foundation for your studies anyway, they aren't supposed to cover the material that the course books already talk about at length. I also think that proofs make much more sense after you have already tried a few example problems - they shouldn't be this mysterious mess of symbols and definitions, they should actually mean something and become obvious to you after you have checked them a couple times, otherwise they are useless.
I love your site, and intend to study all of your math, chemistry, materials sciences, and physics courses. Thank you. I love the texts and homework sets!
Thank u so much for sharing this lecture with the world! Recently we reviewed this content in clases but I didn't get it quite good. Now I definitely understand it way better!!!
At 52:00, there should also be a term for gravitational potential energy (PE) of sleeve due to rotation of the rod. The gravitational PE of the sleeve due to stretching is taken into account, but not due to angular motion of the sleeve.
As usual institutions like MIT gets the best professors to go with there top line students, so success is almost guaranteed! My professor never came close to explaining the Lagrangian like this professor.
just wow. goes to show how different universities can be. i went to school for applied math with a concentration in stats, so i ended up having to taking a lot of physics classes because those met a lot of my pre-reqs for my degree. and not once in any of my upper division physics classes, did the prof ever mention how you need to test first to see if you can use a lagrangian. apparently they just always gave us problems where it worked, and they just left that entire part out.
This is great lecture if u wanna visualise and reason... And do things systematically... Greatful to the lecturer and the organisation to make it available to the world...
Where does the coreolis term (2M2*X1..) comes from , in the therm 1 of lagrange equation for the theta component? I just don't see it in the derivatives...
I followed this through and worked the examples ... in the final collection of d(δΤ/δx)/dt terms there is a Coriolis component 2*m2*x*(dx/dt)*(dθ/dt) to which he refers (at 1:14:46). I cannot see where this was derived in the KE term at 58:00 nor thereafter. Can someone help me by telling me what I am missing?
Excellent lecture.However, I'm in trouble understanding Hamilton's principle and Kane/Jourdain 's Principle. Is there any lecture including these content?
thank you for the explanation. i was following lectures from the start. I found that there may be lecture missing about how to calculate KE and PE for translating and rotating frames. you keep on referring that lecture like " as we calculated in previous lecture etc etc". will you please add that lecture or give me some reference which is more alike to your previous lecture to successfully calculate KE and PE for any system.. please help.
According to J. L Meriam (Dynamics), which stated the Lagrange Equation based on L =T-V is valid for conservative forces only. For non conservative forces the Lagranger Equation shall modified for T (kinetic energy) not L. Please advise.
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Thank you FRANCO FERRUCCI. I was becoming bored until I increased the speed. Now he's become a much better lecturer. Perhaps some other lectures would be more interesting with similar treatment !!!!!!!!!!!!!
18:12 that is because the rotations are not conmutative. Furthermore, 2 rotations is just a subspace of Lie Algebra, se(3), of Euclidean Group, SE(3), to be holonomic you need the movement be a subalgebra of Lie Algebra, like 3 rotations (spherical) or general planar motion (x and y traslations y z rotation) or planar traslation etc.
I had the happy opportunity to have a great math teacher already at the age of 9. And his classes were fundamental to me until the master's degree, already 27 years old. Congratulations to all the great masters of mathematics. BRAZIL BRASÍLIA
The expression for potential energy for the second problem doesn't seem to be consistent for all the terms i.e the spring, sleeve and rod. We need to choose the same initial condition for all the pieces instead of lowest energy positions for each. Since all of them exist as a system. Am I correct?? @ 50 mins
Holy crap that rod and sleeve problem is insane. I don't think my professor would ever expect my class to solve something like that. This is MIT though so I don't know what I expected.
Dane Gil Cabrales I’m in my second year of the theoretical physics bachalor and I’m taking classical mechanics with lagrange, hamilton and special relativity. The course is obligatory.
"In 1766, on the recommendation of Swiss Leonhard Euler and French d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, Prussia, where he stayed for over twenty years, producing volumes of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise on analytical mechanics (Mécanique analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1788-89), written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century. In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy of Sciences. He remained in France until the end of his life. He was instrumental in the decimalisation in Revolutionary France, became the first professor of analysis at the École Polytechnique upon its opening in 1794, was a founding member of the Bureau des Longitudes, and became Senator in 1799." Wikipedia
50:30.. I think the refrence of potential energy for the rod is when theta equals 90 degree, max potential energy. and zero potentional enegry when it's straight down, that's why he got confusion about the signs, so the equation is correct.
From what he said, reference position (= Equilibrium position) is when rod is vertically hanging from the pin. Once oscillation starts, the CG of the rod moves up / down. This difference is taken as change in potential energy. This is what I could make out.
51:56 Why don't have to take account of the length change due to the mass of sleeve? KX=M2g X=M2g/K M2g(L0+L2/2+M2g/K) - M2gX1cos (theta) I thought the reference should be the final possible state? equilibrium state?
At the beginning he refers to better notes "in the cellar" it sounds like. Does anybody know what an where this is? I've got the OCW course materials, but he seemed to me to say there was something better on the net someplace... Thanks, -dlj.
He mentions Stellar which is MIT's course management system. It is a platform for learning, course management and collaboration, serving the MIT community. Most of the Stellar site is not accessible to the public.
There are two components to it's kinetic energy. The first is due to its translational energy, and the second is due to the fact that it's rotating about it's center of mass (while simultaneously translating). So you are correct that A is the axis of rotation for it's entire motion, but to simplify the calculations, the translational motion is treated separately from the rotational motion. This is because Izz wrt A of the sleeve would be time dependent in the inertial frame, but Izz wrt G is not. It's essentially using superposition to isolate a fixed point of rotation.
The conceptual descriptions here are cogent and systematic, but I think the jump from a spring pendulum to that rod/sleeve problem serves to confuse rather than make anything clearer. I understand wanting to give students a challenging problem so that others are easy by comparison, but there seems to me to be too much to keep track of in that problem-rotation, driving force etc.-to solidify the concepts by example. You lose the forest in the trees. I think a more intermediate problem might have been useful to solve to completion.
Where does the professor takes this force [F(t)=F_0 cos (omega t)] from? (video: 1:06:17) Who does exert (apply) it? Is it a new datum of the problem? Thank you, nice video.
Can someone explain why you need the theta dot times x1 at 55:52? I thought the rotational kinetic energy for the sleeve is accounted for in the first term.
What I understood is that we should account for two movements of M2.. One along the rod (With a velocity of x dot) and also rotating about the hinge along with the rod.. (Hence has a velocity component of (v = r * omega used in circular motion) i.e. x1 times theta dot.
Because Izz wrt A would be time dependent in the intertial frame. So instead he used superposition to treat the translational energy and rotational energy separately, and therefore simplify the problem by only considering Izz wrt G, which is constant
As far as I understood, at equilibrium, M2 doesn't cause any displacement in the spring. The equilibrium point is taken at L0 => Unstretched length of spring
At 50:10 he clearly says that 'it is the change in height' that the rod goes through - so the expression gives 'change' in potential energy. However, that is not what we are aiming to write; as per my understanding, we are writing the 'potential energy' of the system, not the change in it. If any of you has an explanation, please share with me.
Anurag Anad: Potential energy can be referred relative to any chosen origin; it is not an absolute quantity as you seem to think. Only changes in potential energy have any physical significance.
step 3 @ 22:18 could be confusing as he wants you to find T AND V, not T PLUS V - a very different thing. Seems a trivial gripe I know, but this could be a real barrier to progress if reviewing notes later
Thank you so much for this video! i´m an student for the upm (universidad politécnica de madrid), in spain. If there are any videos about hit transfer i would apreciate it.
Try going through "Elementary Applied Partial Differential Equations With Fourier Series And Boundary Value Problems" by Richard Haberman for any help in heat transfer theory. I found this book extremely helpful with explanations :)
We are not sure why RU-vid is suggesting something other than the proper playlist for this course. Here is lecture 14: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qrbCpv3Sv34.html
This lecture seems to be very 'In Depth". It gives a good idea of how to completely analyze a system. The derivations may be a bit too in depth for some people.. Perhaps a brief overview of the various concepts would be useful. I can see how this is a lecture that might be appropriate for students who are studying either Engineering or Science.
There is two stages in engineer´s life; before and after knowing what a Lagrangian is as well as its practical applications. Vandiver is quite a good choice. Thank you!!!
