The Multiple Orbits Panel is opened by
selecting the Multiple Panel menu item located on the Panels menu
on the Command Window.
The user selects a region of the product of the phase space and parameter
space. The size of this region is
determined by the size field for that variable or parameter.
The region is centered around the point specified in the
Selected Point Window. The method by which points in this region
are selected depends on the load option. When set to Rectangle, then 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. When set to Region, then a ``box'', including its interior, is selected
the dimension of the box depends on the number of coordinates which have Number
of Points specifed greater than 1. In either case, the lengths of each coordinate
edge of the selected region will be twice the value in the Size field. This
field should be thought of as expressing the radius of the region in each coordinate
dimension. Each edge is discretized by the Number of Points value specified
for that coordinate. The result is a grid of points (or outline of a rectangle)
which make up a set of selected points.
In the case when a region is selected, then the total number of points will be the
product of the values in the Number of Points fields.
If a transfomation other than Identity is selected, then each of these points will
be passed through this filter. Transformations may be defined so that these initial
conditions 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''.
Initial multiple points may also be loaded by using the mouse interface.
Dragging the Ctrl-Select mouse button in a TwoD View Window will draw a rectangle
in the viewing canvas. Upon release of the mouse button, a notice will
appear allowing the user several choices. The selections are Forwards,
Backwards, and Cancel. If the user selects Forwards or Backwards, then
the selected point as displayed in the Selected Point Window is updated
as if the user had selected the center point of the rectangle. The Size
fields on the Multiple Panel of the coordinates in the TwoD View Window
are updated to reflect the size of the user selected box. Then a set of
points are loaded and trajectories are computed, either forwards or backwards
as selected. If the user had selected Cancel, then no action is taken.