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‫Welcome back.

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‫Let's now expand on our knowledge about rotation matrices into 2D, you rotate a body frame with respect

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‫to the inertia frame, only about one axis.

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‫Usually it's about the Z axis because usually your 2D plane is an X Y plane.

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‫And that means that you rotate about the Z axis here that points towards you.

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‫But it doesn't have to be like that if you have a 3D frame and you define positive rotation.

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‫In other words, you use a positive value for an angle, for instance, plus five radians and not minus

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‫five radians, which would be a negative rotation.

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‫If you say that positive rotation around each axis occurs according to the right hand rule, then you

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‫would positively rotate about each axis like this positive rotation about the x axis, positive rotation

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‫about the Y axis, and positive rotation about the Z axis.

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‫If you use your right hand and you grab these axis with your right hand in a way like the rotation happens,

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‫then your thumb would point in the positive X, Y and Z direction.

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‫And that means that negative rotations would happen like this negative rotation about the X axis, negative

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‫rotation about the Y axis, and negative rotation about the Z axis.

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‫So if you use your right hand now, then your thumb would point in the opposite directions.

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‫And now if you think about it, then you can have three different cases for two dimensions.

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‫You can have the most usual case, which is looking directly into the Z axis, using the right hand

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‫rule when rotating about the Z axis.

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‫You can see where positive rotation is and where negative rotation is, but you can also directly look

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‫into y axis.

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‫Then the to the projection would look like this.

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‫Notice how positive and negative rotations occur now according to the right hand rule.

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‫Just take that 3D frame here and just rotate it in such a way so that you would be directly looking

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‫into the Y axis and you will see it.

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‫And finally, as an exercise, do the same thing with the x axis.

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‫Imagine that you are directly looking into the X axis and draw the to the projection for it with positive

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‫and negative rotations according to the right hand rule.

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‫See you in the next video.