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