‫Welcome back.
‫Let's now expand on our knowledge about rotation matrices into 2D, you rotate a body frame with respect
‫to the inertia frame, only about one axis.
‫Usually it's about the Z axis because usually your 2D plane is an X Y plane.
‫And that means that you rotate about the Z axis here that points towards you.
‫But it doesn't have to be like that if you have a 3D frame and you define positive rotation.
‫In other words, you use a positive value for an angle, for instance, plus five radians and not minus
‫five radians, which would be a negative rotation.
‫If you say that positive rotation around each axis occurs according to the right hand rule, then you
‫would positively rotate about each axis like this positive rotation about the x axis, positive rotation
‫about the Y axis, and positive rotation about the Z axis.
‫If you use your right hand and you grab these axis with your right hand in a way like the rotation happens,
‫then your thumb would point in the positive X, Y and Z direction.
‫And that means that negative rotations would happen like this negative rotation about the X axis, negative
‫rotation about the Y axis, and negative rotation about the Z axis.
‫So if you use your right hand now, then your thumb would point in the opposite directions.
‫And now if you think about it, then you can have three different cases for two dimensions.
‫You can have the most usual case, which is looking directly into the Z axis, using the right hand
‫rule when rotating about the Z axis.
‫You can see where positive rotation is and where negative rotation is, but you can also directly look
‫into y axis.
‫Then the to the projection would look like this.
‫Notice how positive and negative rotations occur now according to the right hand rule.
‫Just take that 3D frame here and just rotate it in such a way so that you would be directly looking
‫into the Y axis and you will see it.
‫And finally, as an exercise, do the same thing with the x axis.
‫Imagine that you are directly looking into the X axis and draw the to the projection for it with positive
‫and negative rotations according to the right hand rule.
‫See you in the next video.