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\[ \begin{align} ( & - \frac{v^2}{R}\ cos( P_a ) - v\ \Omega\ cos( S_a )\ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) - v\ \Omega\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) ) \\ \ \\ - ( & - v\ \Omega\ cos( S_a )\ cos( P_a ) - R \Omega^2 \ cos( P_a ), \\ & - v\ \Omega\ sin( P_a ) - R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ cos( P_a ) + R \Omega^2 \ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) + R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) \ \bigr) \\ \end{align} \] (2) の場合 \( cos( S_a ),\ ccs( P_a ),\ sin( P_a ) \) につぎを代入： \[ cos( S_a ) = 0 \\ cos( P_a ) = \frac{ P_x }{ R } \\ sin( P_a ) = \frac{ P_z }{ R } \\ \] \[ \begin{align} ( & - \frac{v^2}{R}\ cos( P_a ) - v\ \Omega\ cos( S_a )\ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) - v\ \Omega\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) ) \\ \ \\ - ( & - v\ \Omega\ cos( S_a )\ cos( P_a ) - R \Omega^2 \ cos( P_a ), \\ & - v\ \Omega\ sin( P_a ) - R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ cos( P_a ) + R \Omega^2 \ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) + R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) \ \ \\ \ \\ ( & - \frac{v^2}{R}\ \frac{ P_x }{ R } , \\ & - v\ \Omega\ \frac{ P_z }{ R }, \\ & - \frac{v^2}{R}\ sin( S_a )\ \frac{ P_z }{ R } ) \\ \ \\ + ( &- R \Omega^2 \ \frac{ P_x }{ R }, \\ & - v\ \Omega\ \frac{ P_z }{ R } , \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ \frac{ P_x }{ R } - R \Omega^2 \ \frac{ P_x }{ R }, \\ & -- 2\ v\ \Omega\ \frac{ P_z }{ R } , \\ & - \frac{v^2}{R}\ sin( S_a )\ \frac{ P_z }{ R } \ \bigr) \\ \end{align} \] \( P_z > 0 \) のとき： \( sin( S_a ) = 1 \) を代入： \[ \begin{align} ( & - \frac{v^2}{R}\ \frac{ P_x }{ R } , \\ & - v\ \Omega\ \frac{ P_z }{ R }, \\ & - \frac{v^2}{R}\ sin( S_a )\ \frac{ P_z }{ R } ) \\ \ \\ + ( &- R \Omega^2 \ \frac{ P_x }{ R }, \\ & - v\ \Omega\ \frac{ P_z }{ R } , \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ cos( P_a ) + R \Omega^2 \ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) + R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) \ \bigr) \\ \ \\ \ \\ ( & - \frac{v^2}{R}\ \frac{ P_x }{ R } , \\ & - v\ \Omega\ \frac{ P_z }{ R }, \\ & - \frac{v^2}{R}\ \frac{ P_z }{ R } ) \\ \ \\ + ( &- R \Omega^2 \ \frac{ P_x }{ R }, \\ & - v\ \Omega\ \frac{ P_z }{ R } , \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ \frac{ P_x }{ R } - R \Omega^2 \ \frac{ P_x }{ R }, \\ & -- 2\ v\ \Omega\ \frac{ P_z }{ R } , \\ & - \frac{v^2}{R}\ \frac{ P_z }{ R } \ \bigr) \\ \end{align} \] \( P_z < 0 \) のとき： \( sin( S_a ) = -1 \) を代入： \[ \begin{align} ( & - \frac{v^2}{R}\ \frac{ P_x }{ R } , \\ & - v\ \Omega\ \frac{ P_z }{ R }, \\ & - \frac{v^2}{R}\ sin( S_a )\ \frac{ P_z }{ R } ) \\ \ \\ + ( &- R \Omega^2 \ \frac{ P_x }{ R }, \\ & - v\ \Omega\ \frac{ P_z }{ R } , \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ \frac{ P_x }{ R } - R \Omega^2 \ \frac{ P_x }{ R }, \\ & -- 2\ v\ \Omega\ \frac{ P_z }{ R } , \\ & - \frac{v^2}{R}\ sin( S_a )\ \frac{ P_z }{ R } \ \bigr) \\ \ \\ \ \\ ( & - \frac{v^2}{R}\ \frac{ P_x }{ R } , \\ & - v\ \Omega\ \frac{ P_z }{ R }, \\ & \frac{v^2}{R}\ \frac{ P_z }{ R } ) \\ \ \\ + ( &- R \Omega^2 \ \frac{ P_x }{ R }, \\ & - v\ \Omega\ \frac{ P_z }{ R } , \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ \frac{ P_x }{ R } - R \Omega^2 \ \frac{ P_x }{ R }, \\ & - 2\ v\ \Omega\ \frac{ P_z }{ R } , \\ & \frac{v^2}{R}\ \frac{ P_z }{ R } \ \bigr) \\ \ \\ \ \\ \end{align} \] (4) の場合 \[ cos( S_a ) = \frac{ P_y }{ \sqrt{ R^2 - P_x^2 } } \\ sin( S_a ) = \frac{ P_z }{ \sqrt{ R^2 - P_x^2 } } \\ cos( P_a ) = \frac{P_x }{R } \\ sin( P_a ) = \frac{ \sqrt{ R^2 - P_x^2 } }{ R } \\ \] \[ \begin{align} ( & - \frac{v^2}{R}\ \frac{P_x }{R } - v\ \Omega\ \frac{ P_y }{ \sqrt{ R^2 - P_x^2 } }\ \frac{P_x }{R }, \\ & - \frac{v^2}{R}\ \frac{ P_y }{ \sqrt{ R^2 - P_x^2 } }\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R } - v\ \Omega\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R }, \\ & - \frac{v^2}{R}\ \frac{ P_z }{ \sqrt{ R^2 - P_x^2 } }\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R } ) \\ \ \\ - ( & - v\ \Omega\ \frac{ P_y }{ \sqrt{ R^2 - P_x^2 } }\ \frac{P_x }{R } - R \Omega^2 \ \frac{P_x }{R }, \\ & - v\ \Omega\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R } - R \Omega^2 \ \frac{ P_y }{ \sqrt{ R^2 - P_x^2 } }\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R }, \\ & 0 ) \\ \ \\ =\ & \bigl( \ - \frac{v^2}{R}\ cos( P_a ) + R \Omega^2 \ cos( P_a ), \\ & - \frac{v^2}{R}\ cos( S_a )\ sin( P_a ) + R \Omega^2 \ cos(S_a)\ sin( P_a ), \\ & - \frac{v^2}{R}\ sin( S_a )\ sin( P_a ) \ \bigr) \\ \end{align} \] \[ \begin{align} \bigl( & - \frac{v^2\ P_x}{R^2} - v\ \Omega\ \frac{ P_x\ P_y }{ R\ \sqrt{ R^2 - P_x^2 } }\ , \\ & - \frac{v^2\ P_y}{R^2} - v\ \Omega\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R }, \\ & - \frac{v^2\ P_z}{R^2} \bigr) \\ \ \\ - ( & - v\ \Omega\ \frac{ P_x\ P_y }{ R\ \sqrt{ R^2 - P_x^2 } } - \Omega^2\ P_x, \\ & - v\ \Omega\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R } - \Omega^2 \ P_y, \\ & 0 ) \\ \ \\ = \bigl( & - \frac{v^2\ P_x}{R^2} - 2\ v\ \Omega\ \frac{ P_x\ P_y }{ R\ \sqrt{ R^2 - P_x^2 } } - \Omega^2\ P_x, \\ & - \frac{v^2\ P_y}{R^2} - 2\ v\ \Omega\ \frac{ \sqrt{ R^2 - P_x^2 } }{ R } - \Omega^2 \ P_y, \\ & - \frac{v^2\ P_z}{R^2} \bigr) \\ \end{align} \]