\[ v_x = v\ cos( \tau )\\ v_y = v\ sin( \tau )\\ \ \\ \ \\ w_x = 0 \\ w_y = r\ \Omega \\ \] \[ v'_x = v\ sin( b ) \\ v'_y = v\ cos( b ) \\ \] ここで \[ \Omega \Delta t + ( b + \tau ) = \frac{ \pi }{ 2 } \\ \Longrightarrow \ b = \frac{ \pi }{ 2 } - ( \tau + \Omega \Delta t ) \\ \ \\ cos( b ) = sin (\tau + \Omega \Delta t ) \\ \quad = sin(\tau) cos(\Omega \Delta t) + cos(\tau) sin(\Omega \Delta t) \\ \ \\ sin( b ) = cos ( \tau + \Omega \Delta t ) \\ \quad = cos(\tau) cos(\Omega \Delta t) - sin(\tau) sin(\Omega \Delta t) \] なので， \[ v'_x = v\ sin( b ) = v\ ( cos(\tau) cos(\Omega \Delta t) - sin(\tau) sin(\Omega \Delta t) ) \\ v'_y = v\ cos( b ) = v\ ( sin(\tau) cos(\Omega \Delta t) + cos(\tau) sin(\Omega \Delta t) ) \\ \] さらに， \[ \begin{align} w'_x = & - | {\bf{w'}} |\ sin( a + \Omega\ \Delta t ) \\ = & - ( \overline{ OP'}\ \Omega )\ ( sin(a)\ cos(\Omega \Delta t) + cos(a)\ sin(\Omega \Delta t) \\ \ \\ w'_y = & \ | {\bf{w'}} |\ cos( a + \Omega\ \Delta t ) \\ = & \ ( \overline{ OP'}\ \Omega )\ ( cos(a)\ cos(\Omega \Delta t) - sin(a)\ sin(\Omega \Delta t) ) \\ \end{align} \] 
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