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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>tangent</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="tangent"> linearization of a dynamical system at an equilibrium point</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[f,g,newm]=tangent(ff,xe,[ue])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>ff</PARAM_NAME>
        <PARAM_DESCRIPTION>
         <SP>: a string which gives the name of the Scilab function which  codes
	    the system, or the fuunction itself.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>xe</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: column vector which gives the equilibrium point for the value ue of the parameter</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>ue</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real value.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>f, g</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: two matrices for the linearised  system  <VERB>dxdot=f.dx + g.du</VERB></SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>newm</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: A new macro of type [y]=newm(t,x,u) which computes the field of the linearised system  (newm(t,xe,ue)=0)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    linearises around the equilibrium point <VERB>(xe,ue)</VERB> the vector field of 
    the dynamical system given by a Scilab macro <VERB>ff</VERB>, <VERB>xdot=ff(t,x,[u])</VERB>.
    The dynamical system is supposed to be autonomous.</P>
  </DESCRIPTION>
</MAN>
