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First we can use the definitions of w, u, alpha, and beta to define $$ \frac{w}{u} = \tan\alpha $$ $$ u = Vcos(\alpha)cos(\beta) $$ Now lets look closer at the first equation you provided using the definitions above: $$\frac{d\alpha}{dt} = \frac{1}{1+\frac{w^2}{u^2}} \left(\frac{w'}{u}-\frac{u'w}{u^2}\right) = \frac{1}{1+\tan^2\alpha} \left(\frac{w'}{...


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