1
00:00:00,500 --> 00:00:12,230
‫However, what if I sex now equals two kilograms times meter squared, then I y y equals.

2
00:00:13,280 --> 00:00:15,680
‫Three kg tanks, meter squared.

3
00:00:16,800 --> 00:00:26,640
‫And ices equals five kilograms times meter squared and 5.8 feet on that and side that are still equal.

4
00:00:26,850 --> 00:00:39,360
‫And there are one radians per second, then h x, h y and z equal the mass moment of inertia matrix

5
00:00:39,570 --> 00:00:40,260
‫times.

6
00:00:41,230 --> 00:00:50,110
‫The angular velocity vector and you're left with two, three and five kg meter squared per second.

7
00:00:51,070 --> 00:00:59,230
‫Now you can clearly see that the angular momentum vector and the angular velocity vector.

8
00:00:59,830 --> 00:01:06,310
‫They have different directions, and that's because you can't extract that constant anymore.

9
00:01:07,240 --> 00:01:14,290
‫You can see that the vector one one one clearly has a different direction compared to a vector that

10
00:01:14,290 --> 00:01:16,600
‫has elements two, three and five.

11
00:01:17,930 --> 00:01:25,190
‫And you can imagine that things can be even worse if you're products of inertia are not zeros.

12
00:01:26,210 --> 00:01:36,470
‫In general, if you have an object and your angular momentum, vector has a different direction compared

13
00:01:36,470 --> 00:01:42,200
‫to your angular velocity vector, then that's not good.

14
00:01:43,570 --> 00:01:48,310
‫Because that will make the rotation of the object not stable.

15
00:01:49,480 --> 00:01:54,400
‫The rotation will not be about any consistent direction, it will tumble.

16
00:01:55,530 --> 00:02:01,110
‫Meaning that at some point your angular velocity will be in this direction.

17
00:02:01,500 --> 00:02:05,340
‫Then at another point, it will be in this direction.

18
00:02:06,090 --> 00:02:08,610
‫And then maybe in this direction.

19
00:02:09,570 --> 00:02:19,230
‫So when you're dealing with rotations in 3-D, then it is recommended that you design your things in

20
00:02:19,230 --> 00:02:28,410
‫such a way that your angular momentum vector would be as closely as possible to your angular velocity

21
00:02:28,410 --> 00:02:35,610
‫vector so that you wouldn't have big differences there and you could achieve that by, for example,

22
00:02:36,090 --> 00:02:38,340
‫only rotating about one axis.

23
00:02:38,490 --> 00:02:49,410
‫Let's say that you only rotate about x axis and you make the y axis and z axis rotations zero gradients

24
00:02:49,410 --> 00:02:50,190
‫per second.

25
00:02:50,790 --> 00:02:54,210
‫In that case, you will have two here.

26
00:02:54,930 --> 00:02:56,790
‫But here you will have zero.

27
00:02:57,180 --> 00:02:59,820
‫And here you will have zero as well.

28
00:03:01,000 --> 00:03:08,350
‫And then your angular velocity vector is one zero zero and then your angular momentum vector is two

29
00:03:08,350 --> 00:03:13,930
‫zero zero, and then they are in the same direction in the X direction.

30
00:03:14,680 --> 00:03:17,770
‫And that makes the rotation much more stable.

31
00:03:18,670 --> 00:03:26,890
‫So now that you know what angular momentum is, we can look at the law that allows us to derive equations

32
00:03:26,890 --> 00:03:29,290
‫of motion for the rotational motion.