RelatedPages.html

Go to the documentation of this file.

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
/*!
\page pg-example Example Codes
<!---------------------------------------------------------------------------!>
\section st-quat Example of quat 
\include quat/main.cpp
<br><br>

<!---------------------------------------------------------------------------!>
\section st-vec Example of vec
\include vec/main.cpp
<br><br>

<!---------------------------------------------------------------------------!>
\section st-mat Example of mat
\include mat/main.cpp
*/

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
/*!
\page pg-convert How to Convert "quat to vec" and "vec to quat"
<!---------------------------------------------------------------------------!>
<h2>im</h2>
<code>vec im(const quat & q)</code><br>
Pull out the imaginary part of q, and put it into v.
<center><code>v =im(q);</code></center>
\f[
  \overrightarrow{v}= \left\{ q_x, q_y, q_z \right\}
\f]

<!---------------------------------------------------------------------------!>
<h2>vr2q</h2>
<code>quat vr2q(const vec & v, const double & r)</code><br>
Put v into im(q), and put r into q.r .<br>
<center><code>q =vr2q(v,r);</code></center>
\f[
  \mathbf{q}= \left[ v_x, v_y, v_z; r \right]
\f]

<!---------------------------------------------------------------------------!>
<h2>vt2q</h2>
<code>quat vt2q(const vec & u, const double & phi)</code>
The rotation quaternion, which axis direction is v and angular is theta.
<center><code>q =vt2q(u,phi);</code></center>
\f[
  \mathbf{q}
= \left[
  \frac{{u_x}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right),
  \frac{{u_y}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right),
  \frac{{u_z}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right);
  \cos \left( \frac{\phi}{2} \right) \right]
\f]

*/

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
/*!
<!--
\page pg-attitude Attitude Quaternion
The following mathod to handle quaternions as attitude expressions is just 
<!---------------------------------------------------------------------------!>
<h2>Definition of Attitude Quaternion</h2>
Let \f$A\f$ and \f$B\f$ be the coordinate-systems.
When the following equation is true for any vector \f$\vec{v}\f$,
\f${}^AB\f$ is defined as the attitude of \f$B\f$ coordinate-system on \f$A\f$ coordinate-system. 
\f[
[{}^A\vec{v};0] ={}^AB [{}^B\vec{v};0] \overline{{}^AB}
\f]

Let inertial coordinate-system
-->
*/

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
/*!
\page pg-rotate How to Rotate "vec"
<!---------------------------------------------------------------------------!>
<h2>rotate</h2>
<center><img src="../image/rotate.png" alt="rotate.png"></center>
To calculate the components of the rotated vector of v around vector u by phi[rad] in right-handed screw rule, 
use the following code. 
<center><code>v_after =rotate(v_before, vt2q(u, phi));</code></center>

\f[
\overrightarrow{v}_\mathrm{after}
 =\mathbf{R}(\overrightarrow{u}, \phi) \overrightarrow{v}_\mathrm{before} \overline{\mathbf{R}(\overrightarrow{u}, \phi)}
\f]
where \f$\mathbf{R}\f$ is 
\f[
\mathbf{R}(\overrightarrow{u}, \phi)
= \left[
  \frac{{u_x}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right),
  \frac{{u_y}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right),
  \frac{{u_z}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right);
  \cos \left( \frac{\phi}{2} \right) \right]
\f]


<!---------------------------------------------------------------------------!>
<!--
<h2>orbit</h2>
<center><img src="../image/orbit.png" alt="orbit.png"></center>
To calculate the components of vector v on a different coordinate system, 
use the following code. 
<center><code>Av =orbit(Bv, AB);</code> or <code>Av =orbit(Bv, conj(BA));</code></center>

\f[
  {}^A\overrightarrow{v}
  ={}^A{B} {}^B\overrightarrow{v} \overline{{}^A{B}}
  =\overline{{}^B{A}} {}^B\overrightarrow{v} {}^B{A}
\f]
where \f${}^A{B}\f$ and \f${}^B{A}\f$ are attitude quaternions.
--!>
*/

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
/*!
<!--
\page pg-nt Short Mathematical Introduction for Quaternion 
--!>
*/

---