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In this video, we will try to apply the lessons, the lessons that we have learned about rotation methods

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into practice.

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We will use the Pethokoukis Robotics Library.

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So let's start with the rotation metrics around X.

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As you can see, the rotation metrics around X is defined by the Command X.

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We will, uh, define rotation around X Pi over three irradiance, then we will animate this rotation.

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So that's its result.

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As you can see, the rotation is around X.

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That's why X doesn't move, but other X is moving, so let's try it with the minus pi over three.

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The rotation should be opposite.

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Excuse me.

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OK.

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As you can see, the rotation is opposite.

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So let's do that with the same thing, but with y axis or y equals two rotation burned by PI over three.

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No, the y axis doesn't move

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on, mate.

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OK, well, let's check what will happen.

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As you can see, no one axis doesn't move.

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There are others.

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Other axis movements do the same with my surroundings.

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As you can see, the rotation is in opposite direction.

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Let's try the same thing with that axis.

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OK, merge three or z and animate opposite.

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Let's run this section.

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As you can see now, the rotation is around z axis and stuff with minus.

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As you can see, we get the opposite rotation.

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So let's check the properties of rotation mattresses.

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So first of all, let's define the rotation mattress, for example, our X rotation x pi over three.

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OK, then let's define it.

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Let's check whether the combs are mutual or thickening.

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We will use DOT product in order to analyze this result because the product of orthogonal vectors are

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zero because cosine of 90 is equal to zero.

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So let's check the result of the dot product of columns of rotation metrics.

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So, OK, we really do the first and second row columns first.

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OK, let's check this answer.

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What we will get?

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OK.

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Let's run this section.

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Excuse me.

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This is one and one so well.

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And two, as you can see, we go zero.

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So, OK, let's do the same with the product.

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Let's do the same with one and three.

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Okay.

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Well, and see first and third rows press of line.

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OK.

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As you can see, we got zero.

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So let's check if the seam is valid for rows.

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Let's do this one.

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First row and second row.

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Let's check press have line.

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As you can see, we got zero again and let's check the first row and third row.

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F9 and as you can see, we saw Bruce and columns are mutual orthogonal, so let's check also determinant

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of our rotation matrix, which is very important.

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It has to be one if you remember correctly.

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Let's run F9.

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OK, this determinant of our rotation matrix.

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OK, we'll check the non-committal commentary tier of rotation practices.

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What's known continuity of rotation references.

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Let's define tool rotation methods for, for example, the first one is rotation around X Pi, over

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three to radiance and the R Y equals rotation of y around, uh, around y axis pi four three degrees

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radius.

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Excuse me.

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So let's first write this one r x y is defined as x multiplied by or, as you know, the multiplication

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of rotation mattresses is also rotation method.

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So our X Y is rotation matrix.

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And also let's define R y x, which is the ordering is opposite of our x y y multiplied by R X.

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So let's see the results of these two rotation mattresses on the Mate 10 Mate X Y.

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Let's check first this one.

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Let's run this section as you can see it, this is our oral rotation for rotation.

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Let's see again, this is the whole rotation.

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Be careful.

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Now we will check R y x.

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As you can see, the total different rotation that's around once again.

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OK.

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This is called non-committal of rotation mattresses.

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This is a property, one of the properties of rotation mattresses.

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Why?

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What does it mean if we change the ordering of rotations?

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The resultant rotation is not the same.

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It will be quite different, as you can see from this code.

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OK, let's check the composition of rotation methods first.

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We will define two rotation mattresses.

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OK, let's copy this one.

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OK, and then we will first do a rotation about current frames.

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So post post multiplication, so on x y equals two or x multiplied by r y.

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So we will first rotate about our X, then we will rotate the newly created frame about Y of the current

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frame, not the fixed frame.

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OK, first let's try to OK, let's try to animate

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x one before animate.

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Let's try to predict the answer.

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So let me come to here.

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OK.

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This is our first axis result.

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This is our initial axis we created first or initial, or it can be a little different.

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Then we try to uh, as you can see, we pi over two degree irradiance.

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We rotated around x zero axis.

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As you can see, we got this newly created, um, yellow frame, one frame or one frame.

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So then we are rotating this yellow frame about the current y axis.

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So not about this one, but about this, uh, y axis.

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We will rotate our newly created frame about this, uh, y axis because this is the current frame,

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so our resultant rotation will be like that.

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So let's check if this is correct.

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OK, let's run this session, OK?

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As you can see, we get what we expected.

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As you can see from here.

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So then let's try the opposite.

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So are you OK with multiplication?

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No, I will do or want X equals two or y times are X and animate, excuse me and mate or X.

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OK, first, let's try to predict the answer.

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OK, let's pass this one, OK, this is our first frame.

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Then we rotate about x zero axis.

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Yeah, fixed, uh, frame about the x axis or fixed frame.

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So we've got this one.

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No, the difference from the first one is here, you have to be careful.

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We will now rotate the newly created frame about the not, uh, the y axis of current frame but fixed

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frame.

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So we will rotate our newly created frame.

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So why von about why zero, which is and the uh, which is about the z axis of currently created frame?

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So the z axis of current frame?

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OK, let's try to rotate.

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As you can see now we get this one.

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As you can see, the rotation is around y axis of fixed axis, but a fixed frame, but uh, z axis of

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current frame.

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So let's check if we will get the same answer as we predicted.

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Press of nine.

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First, let's try to OK, no free press, if not, OK.

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As you see, we got what we have expected.

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The rotation was around z axis.

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Uh, current frame.

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Is it axis of current frame?

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But the y axis of what?

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What axis or fixed frame?

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As you can see from here, we expected correctly.

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OK, see you on the next lesson.