DESCRIPTION

MANUAL

APPLET

EXAMPLES

This manual is divided into two major parts:
 

1. Entering the dynamical system

        Manually via the data dialog
        Plain text input of a definition file
        Choosing an example system located at the home server

2. Visualization

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1. Entering the dynamical system

Main menu (embedded within the browser window)

The main menu consists of 4 button, where the first ("Data") opens the data dialog in which the dynamical system must be specified before a visualization can be generated. The phase-plot allows a quick plot of two chosen variables onto a 2D plane, after a system was calculated. Information about this menu is given with the Help-Window.

With NDimViewer it is possible to enter the equations of a dynamical systems in three different ways:

• Manually via the data dialog
• Plain text input of a definition file
• Choosing an example system located at the home server

A short description of the different ways is also obtained by pressing the "Help"-button in the data dialog.

a) Manually via the data dialog
 

As an interactive way the equations can be entered directly within the data dialog. Therefore the checkbox in the top of the dialog has to be set on "Equationsystem" to get the list of equations. Using the buttons on the right side, the list can be extended or modified. In the bottom the method for numerical approximation can be chosen as well as the time-step size, the number of calculated and the number of drawn points.

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b) Plain text input of a definition file
 

When "Text" is chosen to be the input source, an empty text field appears, into which a definition of the system can be entered. This definition consists of 3 sections. In the first, the "Equations"-section, the differential equations of the variables are quoted. Therefore some restrictions must be noticed:

• The length of the variable-names must always be 1
• The valid letters are all from a to z, except e, which is constant (e=2.7182...)
• Parameters are also entered within this section. The notation is the same, except the ´ (first derivation)  is missing
• On the right side the following operations and functions can be used (all case insensitive):

+ - * / ^ abs() acos() actan()  asin() atan() box() ceil() cos() ctan() exp() exp10() floor() ln() log() round() sin() sinc() sqrt() sqr() tan()

The second section ("Start") defines the initial value for each variable. In the third section ("Options") the number of calculated points ("Steps"), the step width ("Stepwidth"), the number of displayed steps ("DisplaySteps") and the approximation method ("Method") are specified. The method can be "Runge-Kutta" or "Euler". [up]

c) Choosing an example system located at the home server

The last way to enter a dynamical system is to choose on of the example-systems. After selecting "URL" in the top of the dialog a button "Choose Example" appears. Pressing this button pops up a list of available examples on the NDimViewer server, which can be selected and calculated.

When a system finally is entered, the calculation starts after pressing the "OK"-button in the bottom of the data dialog. When the calculation is finished an output window is generated containing the visualization. The definition of the system can be modified by re-opening the data dialog and changing the equations and parameters manually.

The phase plot functions in the main menu is a fast method to get a plot of two choosable variables of the system.

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2. Visualization

After the calculation was completed, a GraphOutput-window is opened, which consists the 3D-canvas with the visualization. EPC is chosen to be the default technique, and the observers position is right in front of the graph.

Now the graph can be rotated with the mouse holding the left button.  It is also possible to zoom in and out by holding the ALT-key and pressing the left mouse button. A further interaction type is the direct manipulation of the graph.

Orange spheres can be dragged using the right mouse button to modify the initial values of the system. Depending on the current technique the spheres can be translated along 1 or two axes. While translating the new starting value can be seen in the status line (right lower corner). If the system shall be recalculated with the new starting values, the "RECALC"-button in the right lower corner has to be pressed.

Yellow spheres are used to move so called highlighting markers along the trajectory. Again, they are translated using the right mouse button. While moving along a trajectory again the current state of the system is displayed in the status line.

On the right side of the status line the used technique can be changed within the drop-down list. A change of the technique immediately changes the output window. The annotation of the graph, i.e. the range of each variable, can be hidden and shown using the "Annotation"-checkbox. To reset the position of the camera, the "Reset-Camera"-button locates the camera on the initial position.

The "Properties"-button generates a window containing all information about the currently visualized dynamical system.  Within the options dialog, which is shown by pressing the "Options"-button, it is possible to configure a high number of parameters of the graph:

The options dialog itself is divided into 5 sections, which will be explained separately. The first is the "Scaling"-section. Here the scaling range of each variable can be modified. The "Fit into one Range"-button calculates the minimal range that contains all variables and sets the scaling of each value to this calculated range. On the right side the size of the graph can be changed.

In the "Colors"-section the color of each variable can be changed simply by pressing the specific "Change"-button. Then a window with 16 colors appears, from which one can be chosen. On the right side several options depending on the current techniques can be changed.

It is also possible to add cutting planes into the graph. With the "Add"-button a new instance of a cutting plane is created. The cutting planes can be either be orthogonal to the parallel axes or be defined freely by a normal vector and an offset. Additionally the color and the transparency is changeable.

The arrangement of variables can be changed within the mapping-section of the options dialog. Beside the arrangement which can be changed with the "move up"- and "move down"-button, variables can also be hidden with the "hide->"-button.  With the "<-show"-button a hidden variable can be put back to the visible ones.

In the last section, the "Highlighting"-section, it is possible to set highlighting markers to mark out a specific point in time of the trajectory. The appearance of the marker depends on the current technique. The marker is equipped with a yellow sphere, which is used to drag the marker forward and back in time.