Find the time variation, By taking the cross product of

Find the time variation

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Reference no: EM131383710

Frisbee with resistance Re-solve the problem of the frisbee with resistance (given Problem) by using Euler's equations. [Find the time dependencies of ω₃ and ω²₁ + ω²₂.]

Problem
Frisbee with resistance A (wobbling) frisbee moving through air is subject to a frictional couple equal to K ω. Find the time variation of the axial spin λ (= ω · a), where a is the axial unit vector. Show also that a satisfies the equation

A a X a^·· + K a X a^· + Cλa^·= 0.

By taking the cross product of this equation with a?, find the time variation of |a|. Deduce that the angle between ω and a decreases with time if C > A (which it is for a normal frisbee). Thus, in the presence of linear resistance, the wobble dies away.

Reference no: EM131383710

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