definition_rotation.html 11 KB

<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <title>Definition of the rotation system of a mount &#8212; Mount Control Software 1.0.0 documentation</title>
    <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
    <link rel="stylesheet" href="_static/classic.css" type="text/css" />
    <link rel="stylesheet" type="text/css" href="_static/graphviz.css" />
    
    <script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
    <script src="_static/jquery.js"></script>
    <script src="_static/underscore.js"></script>
    <script src="_static/doctools.js"></script>
    
    <link rel="index" title="Index" href="genindex.html" />
    <link rel="search" title="Search" href="search.html" />
    <link rel="next" title="Classes for celestial mechanics" href="autodoc_celme.html" />
    <link rel="prev" title="Classes for driving mounts" href="autodoc_mount.html" /> 
  </head><body>
    <div class="related" role="navigation" aria-label="related navigation">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="genindex.html" title="General Index"
             accesskey="I">index</a></li>
        <li class="right" >
          <a href="py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="autodoc_celme.html" title="Classes for celestial mechanics"
             accesskey="N">next</a> |</li>
        <li class="right" >
          <a href="autodoc_mount.html" title="Classes for driving mounts"
             accesskey="P">previous</a> |</li>
        <li class="nav-item nav-item-0"><a href="index.html">Mount Control Software 1.0.0 documentation</a> &#187;</li>
          <li class="nav-item nav-item-1"><a href="autodoc_mount.html" accesskey="U">Classes for driving mounts</a> &#187;</li>
        <li class="nav-item nav-item-this"><a href="">Definition of the rotation system of a mount</a></li> 
      </ul>
    </div>  

    <div class="document">
      <div class="documentwrapper">
        <div class="bodywrapper">
          <div class="body" role="main">
            
  <div class="section" id="definition-of-the-rotation-system-of-a-mount">
<h1>Definition of the rotation system of a mount<a class="headerlink" href="#definition-of-the-rotation-system-of-a-mount" title="Permalink to this headline">¶</a></h1>
<div class="section" id="relation-between-celestial-coordinates-and-the-encoders-of-the-mount">
<h2>Relation between celestial coordinates and the encoders of the mount<a class="headerlink" href="#relation-between-celestial-coordinates-and-the-encoders-of-the-mount" title="Permalink to this headline">¶</a></h2>
<img alt="_images/astro_cel_rot_inc1.png" src="_images/astro_cel_rot_inc1.png" />
<p>The <strong>enc</strong> (encoder) system is defined by motor encoders of a telescope mount.
The usual unit is inc (increment).</p>
<p>The <strong>cel</strong> (celestial) system is defined by local apparent celestial coordinates.
The usual unit is deg (degrees).</p>
<p>The choice of the local apparent celestial coordinates type (ha, dec) or (az, elev) depends on the type of the mount (equatorial, altaz).</p>
<p>Note that astronomical coordinates <strong>astro</strong> (ra, dec, equinoxe) of celestial object catalogs are not locals
but the conversion into <strong>cel</strong> system is univoque using celestial mechanic relations.</p>
<p>Many difficulties exist to convert systems <strong>enc</strong> to <strong>cel</strong>:</p>
<blockquote>
<div><ul class="simple">
<li><p>The conversion <strong>enc</strong> to <strong>cel</strong> is not bijective because a pointing direction in the sky <strong>cel</strong> can be realized by two different <strong>enc</strong> obtained by a back flip of the mount. For example, (ha,dec) = (45, 50) corresponds to the same direction than (ha,dec) = (225,130).</p></li>
<li><p>The zero points of <strong>enc</strong> may not coorespond to zero points of <strong>cel</strong>.</p></li>
<li><p>The increasing angles of <strong>enc</strong> may not correspond to the increasing sense of <strong>cel</strong>.</p></li>
</ul>
</div></blockquote>
<p>We must simplfy the conversion between <strong>enc</strong> and <strong>cel</strong> introducting an intermediate universal system which allows to decouple the problems of senses and zero points of encoders with the back flips of the mount.</p>
<p>The conversion of <strong>enc</strong> to <strong>cel</strong> will be realized using the <strong>rot</strong> (rotation) system.</p>
</div>
<div class="section" id="definition-of-the-angles-rotb-rotp">
<h2>Definition of the angles rotb, rotp<a class="headerlink" href="#definition-of-the-angles-rotb-rotp" title="Permalink to this headline">¶</a></h2>
<p>The system of <strong>rotb,rotp</strong> angles is linked to the machanics of the mount axes.
The goal is to have a local spherical coordinate system which have no ambiguity
and easily recognizable on any type of mounts.</p>
<p><strong>rotb,rotp</strong> are spherical coordinates according the trihedron rx,ry,rz:</p>
<blockquote>
<div><ul class="simple">
<li><p>The rz axis is directed toward the mechanical roation pole which is above horizon.</p></li>
<li><p>The (rx,0,ry) plan turns around the rz axis according the <strong>rotb</strong> (basis angle).</p></li>
<li><p>The rx axis is perpendicular to the rz axis and directed toward the hihest elevation (meridian).</p></li>
<li><p>The ry axis is defined by the direct trihedron with rx and rz.</p></li>
<li><p>The (rx,0,rz) turns around the ry axis according the angle <strong>rotp</strong> (polar angle).</p></li>
</ul>
</div></blockquote>
<p>The origin of <strong>rotb,rotp</strong>:</p>
<blockquote>
<div><ul class="simple">
<li><p>The angle rotp=0 is at the visible pole from the observation site (rx,ry,rz) = (0,0,1).</p></li>
<li><p>The angle rotb=0 is at the meridian with (rx,ry,rz) = (1,0,0).</p></li>
</ul>
</div></blockquote>
<p>The sense of <strong>rotb,rotp</strong>:</p>
<blockquote>
<div><ul class="simple">
<li><p>The increasing sense of rotp is direct in the (ry,0,rz) plane observed from the end of the ry axis.</p></li>
<li><p>The increasing sense of rotb is direct in the (rx,0,ry) plane observed from the end of the rz axis.</p></li>
</ul>
</div></blockquote>
<p>Attention, the pointed direction (rotb, rotp) may not correspond to (ha, dec) because the optical tube could be offseted by an angle according the zero points of rotb, rotp.</p>
<dl class="simple">
<dt>The back flip is univokely identified by the sign of rotp. It is the main advantage of the <strong>rot</strong> system:</dt><dd><ul class="simple">
<li><p>side = 1 if rotp&gt;=0</p></li>
<li><p>side = -1 if rotp&lt;0</p></li>
</ul>
</dd>
</dl>
</div>
<div class="section" id="relations-between-rotb-rotp-and-celb-celp">
<h2>Relations between (rotb, rotp) and (celb, celp)<a class="headerlink" href="#relations-between-rotb-rotp-and-celb-celp" title="Permalink to this headline">¶</a></h2>
<div class="section" id="northern-hemisphere">
<h3>Northern hemisphere<a class="headerlink" href="#northern-hemisphere" title="Permalink to this headline">¶</a></h3>
<img alt="_images/rotbp_n.png" src="_images/rotbp_n.png" />
<dl class="simple">
<dt>Relations:</dt><dd><ul class="simple">
<li><p>Hour angle = celb = -rotb</p></li>
<li><p>Declination = celp = 90-abs(rotp)</p></li>
<li><p>Side = sign of rotp</p></li>
</ul>
</dd>
</dl>
</div>
<div class="section" id="southern-hemisphere">
<h3>Southern hemisphere<a class="headerlink" href="#southern-hemisphere" title="Permalink to this headline">¶</a></h3>
<img alt="_images/rotbp_s.png" src="_images/rotbp_s.png" />
<dl class="simple">
<dt>Relations:</dt><dd><ul class="simple">
<li><p>Hour angle = celb = rotb</p></li>
<li><p>Declination = celp = abs(rotp)-90</p></li>
<li><p>Side = sign of rotp</p></li>
</ul>
</dd>
</dl>
</div>
</div>
</div>


            <div class="clearer"></div>
          </div>
        </div>
      </div>
      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
        <div class="sphinxsidebarwrapper">
  <h3><a href="index.html">Table of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">Definition of the rotation system of a mount</a><ul>
<li><a class="reference internal" href="#relation-between-celestial-coordinates-and-the-encoders-of-the-mount">Relation between celestial coordinates and the encoders of the mount</a></li>
<li><a class="reference internal" href="#definition-of-the-angles-rotb-rotp">Definition of the angles rotb, rotp</a></li>
<li><a class="reference internal" href="#relations-between-rotb-rotp-and-celb-celp">Relations between (rotb, rotp) and (celb, celp)</a><ul>
<li><a class="reference internal" href="#northern-hemisphere">Northern hemisphere</a></li>
<li><a class="reference internal" href="#southern-hemisphere">Southern hemisphere</a></li>
</ul>
</li>
</ul>
</li>
</ul>

  <h4>Previous topic</h4>
  <p class="topless"><a href="autodoc_mount.html"
                        title="previous chapter">Classes for driving mounts</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="autodoc_celme.html"
                        title="next chapter">Classes for celestial mechanics</a></p>
  <div role="note" aria-label="source link">
    <h3>This Page</h3>
    <ul class="this-page-menu">
      <li><a href="_sources/definition_rotation.rst.txt"
            rel="nofollow">Show Source</a></li>
    </ul>
   </div>
<div id="searchbox" style="display: none" role="search">
  <h3 id="searchlabel">Quick search</h3>
    <div class="searchformwrapper">
    <form class="search" action="search.html" method="get">
      <input type="text" name="q" aria-labelledby="searchlabel" />
      <input type="submit" value="Go" />
    </form>
    </div>
</div>
<script>$('#searchbox').show(0);</script>
        </div>
      </div>
      <div class="clearer"></div>
    </div>
    <div class="related" role="navigation" aria-label="related navigation">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="genindex.html" title="General Index"
             >index</a></li>
        <li class="right" >
          <a href="py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="autodoc_celme.html" title="Classes for celestial mechanics"
             >next</a> |</li>
        <li class="right" >
          <a href="autodoc_mount.html" title="Classes for driving mounts"
             >previous</a> |</li>
        <li class="nav-item nav-item-0"><a href="index.html">Mount Control Software 1.0.0 documentation</a> &#187;</li>
          <li class="nav-item nav-item-1"><a href="autodoc_mount.html" >Classes for driving mounts</a> &#187;</li>
        <li class="nav-item nav-item-this"><a href="">Definition of the rotation system of a mount</a></li> 
      </ul>
    </div>
    <div class="footer" role="contentinfo">
        &#169; Copyright 2021, astromecca.
      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 3.4.0.
    </div>
  </body>
</html>