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<H1><A NAME="SECTION004220000000000000000"> </A><A NAME="MultOrbWin"> </A><A NAME="mult_window"> </A><A NAME="window__mult"> </A><A NAME="1312"> </A><A NAME="1313"> </A>
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The Multiple Orbits Window
</H1>
<BR>
<DIV ALIGN="CENTER"><A NAME="multiple"> </A><A NAME="1326"> </A>
<TABLE WIDTH="50%">
<CAPTION><STRONG>Figure 2.23:</STRONG>
The Multiple Orbits window.</CAPTION>
<TR><TD>45#45</TD></TR>
</TABLE>
</DIV>
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<P>
<DL>
<DD><P>
<DT><STRONG>Window title:</STRONG>
<DD>DsTool: Multiple orbits
<DT><STRONG>Function:</STRONG>
<DD>The Multiple Orbits window allows the user to select a set of
initial conditions from which to start trajectories.<A NAME="1319"> </A>
<DT><STRONG>Description:</STRONG>
<DD>The Multiple Orbits window is opened by
selecting the Multiple Orbits option from the Panels menu button located
in the Command window. The user selects a region of the product of the phase space and
parameter space centered about the point specified in the Selected Point window.
The user may specify that points be chosen on a regular grid inside
the region or only on the boundary.
In the former case, a ``box'',
including its interior, is selected.
The dimension of the box depends on the number of coordinates which have Number
of points specified greater than 1. The total number of points will be the product
of the values in the Number of points fields. In the latter case, the points will
form only the outline of a rectangle in two dimensions. The two dimensions
selected will be the first two coordinates in the list with the Number of points
specified greater than 1. If there is only one coordinate with Number of points
greater than 1, then the a line segment is selected. If all the Number of points
fields are set to 1, then only the point specified in the Selected Point window
is selected.
Each edge of the set of selected points is discretized by the Number of points
specified for the associated coordinate, and has length twice the value of the Radius field
for that coordinate.
<P>
If a transformation other than Identity is selected, then each of these points will
be passed through this filter. Transformations may be defined so that these points
can be projected onto some submanifold of the whole space or to
create arrays of points which are not in the form of a ``box''.
<P>
Initial multiple points may also be loaded by using the mouse interface.
Dragging the SELECT<A NAME="1320"> </A> button while holding down CONTROL in a 2-D View
window will draw a rectangle
in the viewing canvas. Upon release of the mouse button, a notice will
appear allowing the user two choices. The selections are Load IC's and
Cancel. If the user selects Load IC's, the appropriate Radius fields on the
Multiple Orbits window are changed, and the new initial conditions are loaded.
However, no orbits are computed. If the user selects Cancel, no action is taken.
<P>
<DT><STRONG>Panel items:</STRONG>
<DD>
<UL>
<LI>Images numeric field:
Displays the number of automatic continuations to be performed. If <I>n</I> is
the value of this field, then selecting Forwards or Backwards with <I>n</I>>1 will produce
the same result as selecting Forwards or Backwards with <I>n</I>=1 and then
selecting Continue <I>n</I>-1 times. The default value is 1.
<LI>Transformation stack setting:
Allows the user to choose a transformation to apply to the selected set of points.
If this is set to anything but the identity, then whenever any points are loaded they will
automatically be mapped through the transformation. The transformation functions
must be defined and installed ahead of time. The options are Identity (the default),
Elliptical, and Rotated.
<LI>and parameter read-write text field:
Displays the parameter to pass to the transformation function.
This value will have different effects (or none at all) depending on the
selected function. For the identity function, it has no effect.
The default value is 0.
<LI>Points on boundary only exclusive setting:
Allows the user to choose whether the shape of the region to be selected is
a ``box'' with interior or the outline of a rectangle (only the boundary
of the ``box''). The default is off, so that the shape of the region selected
is a box.
<LI>Radius read-write text fields:
Display the radius of the box in the direction of each variable and parameter.
Note that the side of the box will have twice this length.
<LI>Points numeric fields:
Display the the number of grid points to put along
the specified side or axis of the box.
<LI>Load multiple initial conditions command button:
Loads the set of initial conditions using the current values
on the Multiple Orbits and Selected Point windows.
<LI>Copy final to initial command button:
Loads the final values of the trajectories computed from the
current initial conditions.
<LI>Forwards command button:
Starts the computation of forward trajectories from each initial condition.
If there are no points loaded then points will be loaded as if the user
had first pressed the Load multiple initial conditions command button.
Trajectories are computed according to the specifications on the Orbits window.
<LI>Continue command button:
Extends the trajectories computed by the Forwards or Backwards
command buttons on the Multiple Orbits window.
<LI>Backwards command button:
Starts the computation of backward trajectories from each initial condition.
If there are no points loaded then points will be loaded as if the user
had first pressed the Load multiple initial conditions command button.
Trajectories are computed according to the specifications on the Orbits window.
<LI>Dismiss command button:
Closes the Multiple Orbits window.
</UL></DL>
<P>
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<ADDRESS>
<I>John Lapeyre</I>
<BR><I>1998-09-04</I>
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