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\usepackage{dennou}
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\Dauthor{��������}
\Dtitle{}
\Ddate{1999/06/02}
\begin{document}
{\bf ����٥��ȥ�${\bf X}(t)$��ñ�̥٥��ȥ�${\bf F}$�ȡ�����ñ�̥٥��ȥ��ľ�򤹤�٥��ȥ�${\vec \epsilon}(t)$���Ѥ���
\begin{equation}
{\bf X}(t) = C(t) {\bf F} + {\vec \epsilon}(t),
\label{eqQUEST}
\end{equation}
��ɽ���롥���ΤȤ�${\vec \epsilon}(t)$�ΥΥ��λ���ʿ���ͤ��˾��Ȥʤ�
ñ�̥٥��ȥ�${\bf F}$�����Ȥ�������ϡ���ͭ������˵��夹�뤳�Ȥ򼨤���
}
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\begin{figure}[hbp]
\begin{center}
\Depsf[11.0cm][]{zu.eps}
\caption{
}
\label{zu}
\end{center}
\end{figure}
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��դ�ꡤ
\begin{equation}
\left\{
\begin{array}{ccc}
{\bf F} \cdot {\bf F}&=&1\\
{\bf F} \cdot {\vec \epsilon}(t) &=& 0
\end{array}
\right.
\label{condition}
\end{equation}
������Ω�ġ��ޤ���
\begin{equation}
C(t) = {\bf X}(t) \cdot {\bf F}.
\end{equation}

(\ref{eqQUEST})����ꡤ
\begin{equation}
{\vec \epsilon}(t) = {\bf X}(t) - C(t) \cdot {\bf F}.
\end{equation}

$I=\overline{ {\vec \epsilon}(t)\cdot {\vec \epsilon}(t)}^{t}
$
���֤��ȡ�
\begin{eqnarray}
I&=&\overline{ {\vec \epsilon}(t) \cdot {\vec \epsilon}(t)}^{t}\nonumber\\
&=&\Dinv{T} \int_0^{T} ({\bf X}(t) - C(t) {\bf F}
, {\bf X}(t) - C(t) {\bf F}) dt .\nonumber 
\end{eqnarray}
$I$���˾��Ȥʤ�Τ����Ǥ��롥�饰��󥸥��̤�그��ˡ�ǲ򤯡�
��(\ref{condition})����������Ƥ���Τǡ�

\begin{eqnarray}
I' &=& \Dinv{T}\int_0^{T} \Biggl\{ \Bigl({\bf X}(t) - C(t) {\bf F}
, {\bf X}(t) - C(t) {\bf F}\Bigr) + \mu \left[ ({\bf F} \cdot {\bf F})-1 \right] \Biggr\} dt\nonumber \\
&=& \Dinv{T} \int_0^{T} \Biggl\{ \Bigl({\bf X}(t) - ({\bf X} \cdot {\bf F}) {\bf F}
, {\bf X}(t) - ({\bf X} \cdot {\bf F})  {\bf F}\Bigr) + \mu \left[ ({\bf F} \cdot {\bf F})-1 \right] \Biggr\} dt\nonumber\\
&=& \Dinv{T} \int_0^{T} \Biggl\{ 
({\bf X} \cdot {\bf X}) - 2 ({\bf X} \cdot {\bf F})^2 + ({\bf X} \cdot {\bf F})^2 ({\bf F} \cdot {\bf F})+ \mu [({\bf F}\cdot {\bf F})-1]
\Biggr\} dt\nonumber\\ 
&=& \Dinv{T} \int_0^{T} \Biggl\{ 
({\bf X} \cdot {\bf X}) - ({\bf X} \cdot {\bf F})^2 + \mu [({\bf F}\cdot {\bf F})-1]
\Biggr\} dt.\nonumber 
 \end{eqnarray}
�������äơ�
\begin{equation}
\delta I' = \Dinv{T} \int_0^T \Biggl\{ 
-2 ({\bf X} \cdot {\bf F}) ({\bf X} \cdot \delta {\bf F})
+2 \mu ({\bf F} \cdot \delta {\bf F})
\Biggr\} dt 
\end{equation}
$\delta {\bf F}$�ˤ��ʤ�����ˤϡ�
\begin{equation}
\Dinv{T} \int_0^{T} \Biggl\{
-2 ({\bf X} \cdot {\bf F}) {\bf X}
+2 \mu {\bf F}
\Biggr\} dt =0.
\end{equation}
�������ʬ�ǽ񤯡�
\begin{equation}
\overline{ x_{\alpha}(t) x_{\beta}(t) } F_{\beta}
= \mu F_{\alpha}
\end{equation}
�Ĥޤꡤ
$$A {\bf F} = \mu {\bf F}.$$

\end{document}








