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I need to prove that the acceleration is given by,

[tex]a = -\frac{1}{2} \nabla [(\Omega \times r)^2] [/tex]

I figured it should follow from the fact that,

[tex]a = \frac{du}{dt} = \frac{\partial u}{\partial t} + u \cdot \nabla u = u \cdot \nabla u [/tex]

But I can't work out where to go from there. We are supposed to use Cartesian tensor methods to work it out.

Could anyone help me out?