マスプロパティ計算

複数の質量・重心・慣性行列を統合し単一の質量・重心・慣性行列の組 $[m_{new},$ $_{new},$ $_{new}]$ を計算する演算関数を次のように定義する．

$\displaystyle [m_{new},$ $\displaystyle \mbox{\boldmath {$c$}}$ $\displaystyle _{new},$ $\displaystyle \mbox{\boldmath {$I$}}$ $\displaystyle _{new}] = AddMassProperty( [m_{1},$ $\displaystyle \mbox{\boldmath {$c$}}$ $\displaystyle _{1},$ $\displaystyle \mbox{\boldmath {$I$}}$ $\displaystyle _{1}] ,\hdots, [m_{K},$ $\displaystyle \mbox{\boldmath {$c$}}$ $\displaystyle _{K},$ $\displaystyle \mbox{\boldmath {$I$}}$ $\displaystyle _{K}] )$

(30)

これは次のような演算である．

$\displaystyle m_{new} = \sum_{j=1}^{K}m_{j}$

(31)

$\displaystyle \mbox{\boldmath {$c$}}$ $\displaystyle _{new} = \frac{1}{m_{new}}\sum_{j=1}^{K} m_j$ $\displaystyle \mbox{\boldmath {$c$}}$ $\displaystyle _j$

(32)

$\displaystyle \mbox{\boldmath {$I$}}$ $\displaystyle _{new} = \sum_{j=1}^{K} \left( \mbox{\boldmath {$I$}}_j + m_j \mb... ...dmath {$D$}}(\mbox{\boldmath {$c$}}_{j} - \mbox{\boldmath {$c$}}_{new}) \right)$

(33)

ここで， $)=\hat{\mbox{\boldmath {$r$}}}^T\hat{\mbox{\boldmath {$r$}}}$ とする．

2016-04-05