<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html
  SYSTEM "about:legacy-compat">
<html xmlns:mml = "http://www.w3.org/1998/Math/MathML" lang = "en"><head><meta charset = "UTF-8"/><meta name = "copyright" content = "(C) Copyright 2020"/><meta name = "DC.rights.owner" content = "(C) Copyright 2020"/><meta name = "DC.type" content = "reference"/><meta name = "abstract" content = "Defines coordinate systems with reference to an existing coordinate system or three nodes."/><meta name = "description" content = "Defines coordinate systems with reference to an existing coordinate system or three nodes."/><meta name = "DC.relation" scheme = "URI" content = "../TsoUserMap/tso-m-usr-model-csDef-sb.htm#tso-m-usr-model-csDef-sb"/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-r-cmd-csDef"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>CS_DEF</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script><script type = "text/javascript" src = "../MathJax/MathJax.js?config=DS-default,local/local">
  		/* */
  		</script></head><body onLoad = "highlightSearchTerms();" id = "tso-r-cmd-csDef">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>CS_DEF</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">Defines coordinate systems with reference to an existing coordinate system or three nodes.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-r-cmd-csDef__tso-r-cmd-csDef-localType" id = "toc_rg" title = "">Items for DEF_TYPE = LOCAL</a></li><li><a href = "#tso-r-cmd-csDef__tso-r-cmd-csDef-nodeType" id = "toc_rg" title = "">Items for DEF_TYPE = NODE</a></li><li><a href = "#tso-r-cmd-csDef__tso-r-cmd-csDef-vectorType" id = "toc_rg" title = "">Items for DEF_TYPE = VECTOR</a></li><li><a href = "#tso-r-cmd-csDef__tso-r-cmd-csDef-rmk" id = "toc_rg" title = "">Remark</a></li><li><a href = "#tso-r-cmd-csDef__tso-r-cmd-csDef-expl" id = "toc_rg" title = "">Examples</a></li></ul>
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr></table><table class = "DocTopicsInOtherGuides" id = "table14"><tr><td height = "8px"/></tr><tr><td class = "TopicsTitleNormal">In Other Guides</td></tr><tr><td><a title = "In certain situations, the definition of solids and displacement directions requires the coordinate systems that differ from those defined in the FE model." href = "../TsoUserMap/tso-m-usr-model-csDef-sb.htm#tso-m-usr-model-csDef-sb">Coordinate Systems (CS_DEF)</a></td></tr></table></td></tr></table>




<div class = "body refbody">

<table class = "table" id = "tso-r-cmd-csDef__aa2016319"><caption/><colgroup><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">ID_NAME</span> </p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;name_of_coord_system&gt;</code></p></td>
<td class = "entry"><p>Name of the coordinate system</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">CS_TYPE</span> </p></td>
<td class = "entry"><p>= RECTANGULAR</p><p>= CYLINDRICAL</p><p>= SPHERICAL</p></td>
<td class = "entry"><p>Type of new coordinate system</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">DEF_TYPE</span> </p></td>
<td class = "entry"><p>= LOCAL</p></td>
<td class = "entry"><p><code class = "ph codeph">LOCAL</code> definition refers to an existing coordinate system</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NODE</p></td>
<td class = "entry"><p>Definition using three nodes</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= VECTOR</p></td>
<td class = "entry"><p>Definition using an origin and three vectors</p></td>
</tr>
</tbody></table>

<div class = "section" id = "tso-r-cmd-csDef__tso-r-cmd-csDef-localType"><h2 class = "title sectiontitle">Items for DEF_TYPE = LOCAL</h2>

<table class = "table" id = "tso-r-cmd-csDef__aa2016457"><caption/><colgroup><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">CS_REF</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;name_of_coord_system&gt;</code></p></td>
<td class = "entry"><p>Existing reference coordinate system</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">ORIGIN_123</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;coord_1&gt;, &lt;coord_2&gt;, &lt;coord_3&gt;</code></p></td>
<td class = "entry"><p>Coordinate values of the origin</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">ROTATION_321</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;rot_3&gt;, &lt;rot_2&gt;, &lt;rot_1&gt;</code></p></td>
<td class = "entry"><p>Rotations that should be superimposed on the reference coordinate system</p></td>
</tr>
</tbody></table>
</div>


<div class = "section" id = "tso-r-cmd-csDef__tso-r-cmd-csDef-nodeType"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Items for DEF_TYPE = NODE</h2>

<table class = "table" id = "tso-r-cmd-csDef__aa2016478"><caption/><colgroup><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">CS_AXIS</span></p></td>
<td class = "entry"/>
<td class = "entry"><p>Specifies the axis and the plane defined by the three nodes.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= X_XY</p></td>
<td class = "entry"><p>X-axis and the X-Y plane are defined by the three nodes.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= X_XZ</p></td>
<td class = "entry"><p>X-axis and X-Z plane are defined by the nodes.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= Z_XZ</p></td>
<td class = "entry"><p>Z-axis and X-Z plane are defined by the nodes.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">NODE_ORIGIN </span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;node_id_of_origin&gt;</code></p></td>
<td class = "entry"><p>ID of node which defines the origin</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">NODE_AXIS</span><span class = "ph uicontrol"> </span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;node_id_on_axis&gt;</code></p></td>
<td class = "entry"><p>ID of the node on the axis</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">NODE_PLANE</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;node_id_on_plane&gt;</code></p></td>
<td class = "entry"><p>ID of the node on the given plane and the second axis</p></td>
</tr>
</tbody></table>
</div>


<div class = "section" id = "tso-r-cmd-csDef__tso-r-cmd-csDef-vectorType"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Items for DEF_TYPE = VECTOR</h2>

<table class = "table"><caption/><colgroup><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">ORIGIN</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;coord_1&gt;, &lt;coord_2&gt;, &lt;coord_3&gt;</code></p></td>
<td class = "entry"><p>Coordinate values of the origin</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VECTOR_X</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;coord_1&gt;, &lt;coord_2&gt;, &lt;coord_3&gt;</code></p></td>
<td class = "entry"><p>Direction of the first reference vector.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VECTOR_Y</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;coord_1&gt;, &lt;coord_2&gt;, &lt;coord_3&gt;</code></p></td>
<td class = "entry"><p>Direction of the second reference vector.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VECTOR_Z</span></p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;coord_1&gt;, &lt;coord_2&gt;, &lt;coord_3&gt;</code></p></td>
<td class = "entry"><p>Direction of the third reference vector.</p></td>
</tr>
</tbody></table>
</div>

<div class = "section" id = "tso-r-cmd-csDef__tso-r-cmd-csDef-rmk"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Remark</h2>

<ul class = "ul">
<li class = "li"><p>The rotation matrix given by <code class = "ph codeph">VECTOR_X</code>, <code class = "ph codeph">VECTOR_Y</code>, <code class = "ph codeph">VECTOR_Z</code>
	must have a determinant of 1:</p>
    <p><span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "17" altimg-width = "22" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">abs</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">det</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "[" close = "]" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced><mi class = "- topic/foreign ">=</mi><mi class = "- topic/foreign ">abs</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">det</mi><mfenced open = "(" close = ")" class = "- topic/foreign "><mrow class = "- topic/foreign "><mfenced open = "[" close = "]" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">VECTOR_X, VECTOR_Y, VECTOR_Z</mi></mrow></mfenced></mrow></mfenced></mrow></mfenced><mi class = "- topic/foreign ">=</mi><mi class = "- topic/foreign ">1</mi></mrow></math></span></p></li>
<li class = "li">The rotation angles in the command <code class = "ph codeph">ROTATION_321</code> are in degrees.
    The single rotations are carried out in series around the axis of the local Cartesian coordinate.
    The following figure shows the rotations for <code class = "ph codeph">ROTATION_321 = 180.0, 0.0, 90.0</code>:
    <br/><img class = "image" src = "../TsoCmdImages/coord_sys_rotation.png" width = "420"/><br/></li>
<li class = "li">The longitudinal axis of a cylindrical coordinate system is defined by the z-axis of the referenced rectangular coordinate system.
     Respectively, the polar axis equals the x-axis, as shown in the following image:
    <br/><img class = "image" src = "../TsoCmdImages/cyl_coord_cys_definition.png" width = "340"/><br/></li>
</ul>
</div>


<div class = "section" id = "tso-r-cmd-csDef__tso-r-cmd-csDef-expl"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Examples</h2>

<p>The following command defines a cylindrical coordinate system with origin (10,20,0) with respect to the global Cartesian coordinate system <code class = "ph codeph">CS_0</code>.
   The polar axis and longitudinal axis are obtained by rotating the x-axis and z-axis of <code class = "ph codeph">CS_0</code> respectively by 45° around the z-axis and by 15° around the y-axis of <code class = "ph codeph">CS_0</code>.</p>
<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME      = my_cs_01
  CS_TYPE      = CYLINDRICAL
  DEF_TYPE     = LOCAL
  CS_REF       = cs_0
  ORIGIN_123   = 10.0, 20.0, 30.0
  ROTATION_321 = 45.0, 15.0, 0.0
END_
</code>
</pre>

<p>The following command defines a rectangular (Cartesian) coordinate system
   with origin through the node with ID number 10. The x-axis is defined by the
   nodes 10 and 100. Node 101 defines a point in the x-y plane.</p>
<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME     = my_cs_02
  CS_TYPE     = RECTANGULAR
  DEF_TYPE    = NODE
  CS_AXIS     = X_XY
  NODE_ORIGIN = 10
  NODE_AXIS   = 100
  NODE_PLANE  = 101
END_
</code>
</pre>
<p>The following command defines a rectangular (Cartesian) coordinate system
   with origin (10,10,10). The x-axis is defined by the vector (-1,0,0), y-axis
   with the vector (0,-1,0) and the z-axis with (0,0,-1).</p>
<pre class = "codeblock">
<code class = "ph codeph">
CS_DEF
  ID_NAME  = my_cs
  CS_TYPE  = RECTANGULAR
  DEF_TYPE = VECTOR
  ORIGIN   = 10,10,10
  VECTOR_X = -1,0,0
  VECTOR_Y = 0,-1,0
  VECTOR_Z = 0,0,-1
END_
</code>
</pre>
</div>


</div>

<div class = "related-links"/>
</td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
