Illustrate requirement of constant angles yields trajectory


Falcons flying to attack the prey on ground follow the logarithmic spiral instead of the straight line. This is because their eyes are on 2 sides of the head, and if they required to cock their head to keep their prey in their sight it would increase air resistance. So they fly in the trajectory keeping same angle, 40 degrees, between its tangent and direct line to prey. Illustrate that requirement of constant angles yields the trajectory that is in form of the logarithmic spiral, r=a*e^(b*theta), where r is radial distance to prey and theta is azimuthal angle.

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Mathematics: Illustrate requirement of constant angles yields trajectory
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