definition_rotation.html
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<title>Definition of the rotation system of a mount — Mount Control Software 1.0.0 documentation</title>
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<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>=0</p></li>
<li><p>side = -1 if rotp<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>
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<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>
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