Lagrange in dynamics on a very high level. Anybody want to volunteer, what is Lagrangian dynamics, Julia? >> Yeah, again. >> Okay >> We haven't actually done potential energy yet, but the big thing is kinetic energy, right? We can right, we can get the equations of motion by applying all this stuff and then that we're good, which brings up a question. This always comes up in 50 turn, and now you guys are wiser, smarter older. All right, so if you have no external forces acting on it, then kinetic energy should be constant. Let's assume that for now, so if t dot is equal to zero, can you use this to derive your equations of motion? >> Well, there's only one equation. >> So, if your system is a single particle, maybe there's a spring a dash boat, who knows there's a mass m here, could you then use this to get equations? Yeah, but remember scalar energy is just one equation. So there are cases where you happen to get the right answer And then people 50 10, of course apply it to everything because it worked once it must work always. All right, I wish that was the case. And you know, if you have multiple coordinates, your this is still one equation, you cannot get 15Â°, you know, differential equations from one simple scalar condition, so, just be aware of that. So, what was the Lagrange? We did it in terms of energy right now, Andrew, do you remember what the form was? >> because we're going to see this equation over and over again now for, you know, for the next few weeks. [INAUDIBLE] Right? Okay, so there's that one help him out, anything else Josh? >> It should be a DDT first term and then minus. >> Sorry LT, they'll queue, okay, and what this is equal to? >> If you have any if you only have >> your life isn't that good? >> No, the answer was if you only have conservative forces then this is zero that's not true. Why not? [INAUDIBLE] No >> We haven't discussed constraints yet. So just this equation, when Is this equal to 0? It's not when you only have conservative forces. True. Only non working forces. Yeah. Q okay, and let me just help you guys out. I'm going to put an I here because we may have multiple ones, right? So if you have conservative forces, let's say gravity is in the picture, this is a good review because we're going to see all this again today. If you have gravity in the picture, where does that go? Abby? Yeah, this Q here, right big Q, we have multiple Qs. I blame whoever did this originally, bad choice and letters, but so this would go in here. Right, So josh you were thinking we would have zero on the right hand side, so you're kind of jumping ahead. >> Taking L >> L Exactly. So today we're going to introduce and discuss what if we have some of the forces are conservative because then they are the result of minus the gradient of the potential function with respect to the states must give you this force. And we can see how we can modify that So we're going to get to that, so if you have an L this goes there. But what we've derived so far is this equation, so if you use this, this is whatever forces are acting on the system you put them in, but we don't have to include non working forces. So, you know, things that are implied, enforced polynomial constraints, which is nice. It's a lot of those things drop out and we only have to do the working force is in the end. Right, so that was done on there. So to get kinetic energy, this can be in terms of which variables does kinetic energy depends on. Q dots definitely does it depend on cue? [INAUDIBLE] It can write often we just have M over two X dot squared. Cool, life is good, there's no X in there, but sometimes you will see in examples, like we had that sled moving back and forth with a pendulum hanging from it. But all of a sudden the pendulum and mass velocity is a function of the sled position and rates and angles and all that stuff couples together and all of a sudden states appear. So often, it's just this in simple systems that we look at, but anything a little more complicated, you're going to have the states and the rates of your generalized coordinates that are in there. So how do we get kinetic energy, this is kinetic energy relative to what? How do we always write these things? All right, we ended up having Mi over 2 Ri in dotted with Ri. All right, this is one of the things that we used to derive this. What happened to my first thought? There we go, how was this R defined relative to inertial frame? Right, So just be aware of that, especially if you're doing relative motion. Although those kinds of things, you have to really get the inertial, this is the inertial energy, not the energy of an approaching satellite with respect to the space station or something. This won't work properly, okay, so that means all the stuff you had in 5010, all the basic cinematics still have to be done correctly. And as you've seen many times it's easy to do using rotating frames. So okay, let's see, so then you're going to have to write out Ri as something, and what type of derivative is this Ri dot going to be inertial? Of course, right, so if you have rotating frames transport theorem still has to be in there. So, the biggest source of error I'm seeing is this is really nice, once you have an energy expression you can plug it into Mathematica, it'll grind out those partials and time derivatives and give you these beautiful looking differential equations. And you can solve them and it gives you wonderful plots, I think it must be true. I automated everything, the computer wouldn't lie right, but if you make a mistake in your energies, because you didn't define things properly garbage in garbage out.