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‫Welcome back and here's your answer when you decompose the longitudinal velocity vector and the lateral

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‫velocity vector, then it will become apparent how the answer is found.

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‫We're going to shift the body frame here to match the origins of the body frame and the inertial frame.

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‫And remember, we can shift the body frame around as we please, because when we deal with orientation,

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‫then we don't care about the position of the body frame with respect to the initial frame.

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‫We only care about the angles, how the body frame is oriented with respect to the inertial frame.

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‫And so when we shift our body frame, for example, to this place, then the angle here is the same,

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‫like the angle here.

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‫And that's why you can shift the body frame around as you want, because the angles are the same, the

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‫angles don't change.

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‫And you can see that the inertia frame accident is formed by the positive X component of the longitudinal

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‫velocity and by the negative X component of the lateral velocity.

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‫That is why the value in front of Y dot here is negative.

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‫However, the inertia frame y dot is composed of the positive y component of the longitudinal velocity

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‫and also a positive y component of the lateral velocity.

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‫Both components point up.

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‫OK, so we have represented the big X dot and the big Y dot in terms of small X dot, small Y dot and

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‫the Passi angle.

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‫In other words, we have represented the velocities that were initially in the body frame.

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‫We have represented them in the inertial frame.

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‫But now another thought exercise for you.

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‫Can you think of another way how to represent this relationship?

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‫Can you take this relationship and simply reformulated?

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‫The relationship will be the same.

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‫Tried to put it in a different form and you will see the solution in the next video.

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‫Thank you very much.

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‫And see you there.