1 00:00:00,600 --> 00:00:01,350 ‫Welcome back. 2 00:00:01,860 --> 00:00:10,020 ‫So let's go through this small exercise, then the units for our trust factor, C, t. 3 00:00:11,080 --> 00:00:21,700 ‫It would have the units of Knewton times 2nd squared and then the torque factor would have the units 4 00:00:21,700 --> 00:00:22,240 ‫of. 5 00:00:23,260 --> 00:00:28,600 ‫Newton Meter and second squared. 6 00:00:29,790 --> 00:00:31,120 ‫And it makes sense, right? 7 00:00:31,530 --> 00:00:40,320 ‫So if you take your trust factor C.T. and then you multiply it by an Omega squared, then what you will 8 00:00:40,320 --> 00:00:44,580 ‫get is a thrust force and a thrust force. 9 00:00:44,580 --> 00:00:49,450 ‫Like all other forces, they have a unit of mutants. 10 00:00:50,340 --> 00:01:01,410 ‫And so here you would have Newton's times second squared, which is this one here, times radians squared 11 00:01:02,040 --> 00:01:08,730 ‫over, second squared because the units formiga are radians over second. 12 00:01:09,820 --> 00:01:19,510 ‫Like this, and then if you square them, then it will be radion squared over second squared and then 13 00:01:19,510 --> 00:01:23,830 ‫your second squared will cancel out and you're left with Newton. 14 00:01:24,580 --> 00:01:27,160 ‫Now, remember this radiance? 15 00:01:27,160 --> 00:01:29,020 ‫It's a dimensionless quantity. 16 00:01:30,070 --> 00:01:37,210 ‫Radiance come from a circle where you have a circumference which is in meters, and then you have a 17 00:01:37,210 --> 00:01:40,290 ‫diameter, which is also in meters. 18 00:01:41,140 --> 00:01:48,430 ‫And so, for example, the circumference of a circle divided by the diameter of the circle would give 19 00:01:48,430 --> 00:01:53,050 ‫you pi radiance like this. 20 00:01:53,860 --> 00:02:00,550 ‫But that means that in terms of units, the circumference and then the diameter, you would be dividing 21 00:02:00,850 --> 00:02:10,630 ‫meters by meters which would cancel out and therefore your radiance is in fact dimensionless. 22 00:02:11,440 --> 00:02:21,460 ‫So the other way to look at it is like this radiant squared would be meters squared, over meters squared. 23 00:02:21,470 --> 00:02:23,170 ‫That will also cancel out. 24 00:02:23,380 --> 00:02:25,120 ‫And you're left with Newton's. 25 00:02:26,080 --> 00:02:36,130 ‫And so now if we take this talk factor, CQ, and we multiplied by some kind of Omega squared, then 26 00:02:36,130 --> 00:02:44,560 ‫we will get some kind of moment or some kind of talk, and then the units here would be Knewton times 27 00:02:44,800 --> 00:02:45,520 ‫meters. 28 00:02:46,510 --> 00:02:53,110 ‫And so you would have Knewton times, Meaders times 2nd squared. 29 00:02:53,320 --> 00:02:55,240 ‫That's from here. 30 00:02:55,630 --> 00:03:07,900 ‫And then times you would have again radians squared over second squared and now you will cancel out 31 00:03:08,110 --> 00:03:13,640 ‫the seconds squared and you are left with Knewton times meter. 32 00:03:14,740 --> 00:03:23,850 ‫OK, but now you have these equations here and you can compute your use if you know your omega's. 33 00:03:24,310 --> 00:03:29,720 ‫However, if you remember then we really wanted the opposite thing. 34 00:03:30,310 --> 00:03:34,570 ‫The controller gives you your control inputs. 35 00:03:34,570 --> 00:03:37,780 ‫You one, you two, you three and you four. 36 00:03:38,620 --> 00:03:45,530 ‫And then we need to use these control inputs to get our omega's. 37 00:03:46,450 --> 00:03:51,430 ‫So that means that we have to. 38 00:03:52,690 --> 00:04:02,050 ‫Invert this system of equations and we need to express our omega one, omega to omega three and omega 39 00:04:02,050 --> 00:04:10,690 ‫four in terms of you want you to Q3 and Q4 and that will be your final exercise in this section. 40 00:04:11,560 --> 00:04:19,780 ‫Tried to find this set of equations where you have your omega one, omega two, omega three and Omega 41 00:04:20,020 --> 00:04:29,080 ‫four, and then you will have these four equations here and they will contain all these control inputs. 42 00:04:29,380 --> 00:04:30,250 ‫What would it be? 43 00:04:31,330 --> 00:04:34,180 ‫Thank you very much and see you in the next video.