\[ v_x = v\ cos( \tau )\\ v_y = v\ sin( \tau )\\ \ \\ v'_x = v\ ( cos(\tau) cos(\Omega \Delta t) - sin(\tau) sin(\Omega \Delta t) ) \\ v'_y = v\ ( sin(\tau) cos(\Omega \Delta t) + cos(\tau) sin(\Omega \Delta t) ) \\ \] \[ \frac{ 1 }{ \Delta t }\ \frac{ v'_x - v_x }{ v } \\ \ \\ = \frac{ 1 }{ \Delta t }\ ( ( cos(\tau) cos(\Omega \Delta t) - sin(\tau) sin(\Omega \Delta t) ) - cos( \tau ) ) \\ \ \\ = \frac{ 1 }{ \Delta t }\ ( - cos(\tau)\ ( 1 - cos(\Omega \Delta t) ) - sin(\tau)\ sin(\Omega \Delta t) )\\ \ \\ = - cos(\tau)\ \frac{ 1 - cos(\Omega \Delta t ) }{ \Delta t }\ - sin(\tau)\ \frac{ sin(\Omega \Delta t) ) }{ \Delta t } \\ \ \\ = - cos(\tau)\ ( \Omega^2\ \Delta t )\ \frac{ 1 - cos(\Omega \Delta t ) }{ ( \Omega\ \Delta t )^2 }\ - sin(\tau)\ \Omega\ \frac{ sin(\Omega \Delta t) ) }{ \Omega\ \Delta t } \\ \ \\ \ \\ \longrightarrow \ 0 - sin(\tau)\ \Omega\ \ \ ( \Delta t \rightarrow 0 ) \\ \] \[ \frac{ 1 }{ \Delta t }\ \frac{ v'_y - v_y }{ v } \\ \ \\ = \frac{ 1 }{ \Delta t }\ ( ( sin(\tau) cos(\Omega \Delta t) + cos(\tau) sin(\Omega \Delta t) ) - sin( \tau ) ) \\ \ \\ = \frac{ 1 }{ \Delta t }\ ( - sin(\tau)\ ( 1 - cos(\Omega \Delta t) ) + cos(\tau)\ sin(\Omega \Delta t) )\\ \ \\ = - sin(\tau)\ \frac{ 1 - cos(\Omega \Delta t ) }{ \Delta t }\ + cos(\tau)\ \frac{ sin(\Omega \Delta t) ) }{ \Delta t } \\ \ \\ = - sin(\tau)\ ( \Omega^2\ \Delta t )\ \frac{ 1 - cos(\Omega \Delta t ) }{ ( \Omega\ \Delta t )^2 }\ - + cos(\tau)\ \Omega\ \frac{ sin(\Omega \Delta t) ) }{ \Omega\ \Delta t } \\ \ \\ \ \\ \longrightarrow \ 0 + cos(\tau)\ \Omega\ \ \ ( \Delta t \rightarrow 0 ) \\ \] よって， \[ \frac{ {\bf v'} - {\bf v} }{\Delta t} \longrightarrow ( - v\ \Omega\ sin(\tau),\ v\ \Omega\ cos(\tau) ) \ \ \ ( \Delta t \rightarrow 0 ) \]