Lösung.

  1. Es ist
    $ \mbox{$\displaystyle \dot q = \frac{\text{d}}{\text{d}t} \, \frac v u = \... ...u - v \dot u}{u^2} = \frac{C u^2 - A^{\text{t}}vu - v A u - B v^2}{u^2} $}$
    und damit
    $ \mbox{$\displaystyle \begin{array}{rl} & \dot q + A^{\text{t}} q + q A + ... ...t{t}} vu + vAu + Bv^2 - Cu^2}{u^2} \vspace{3mm}\\ =&0. \end{array} $}$
  2. Es ist
    $ \mbox{$\displaystyle \dot u = (A+Bq)u = Au + Bqu = Au+Bv $}$
    und
    $ \mbox{$\displaystyle \begin{array}{rcl} \dot v &=& \dot q u + q \dot u... ...vspace{3mm}\\ &=& Cu - A^\text{t}qu = Cu - A^\text{t} v. \end{array} $}$