Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 4 / 12A / a

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- Solution a

Solution

Let

{e_{i} (t)}

be an orthonormal basis fixed in

S^{'}

and write

a = a_{i} e_{i}

. A basis vector rotating with angular velocity

ω

satisfies

(\dot{e}_{i})_{S} = ω \times e_{i} .

Differentiating the components and the basis vectors in

S

therefore gives the rotating-frame derivative formula

(\dot{a})_{S} = \overset{a}{˙}_{i} e_{i} + a_{i} ω \times e_{i} = (\dot{a})_{S^{'}} + ω \times a .

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