Summary of important parameters and controls

Main window Menu

 

File

Constants

Compile

Create in another variable

Create array of  IVPs

Clear

Graph

Parameters

Font

Set n-body problem

Help

Demo

 

File submenus

 

New

 

Open 

Open ode file

Load script

Load script file

Open to Connect

Open one of several connected problems

Open special points and…

Differentiate 0 times

Differentiate 1 time

Differentiate 2 times

Assume the conv. radius = radius limit

Save

Save ode file

Save as

Save ode file

Save script

Save script file

Save to clipboard…

The path to script file

The command line with the scrip file

Load data

Load the Results file

Save data

Save the Results file

Save as table

Save the solution in tabulated form

Print

 

 

Explanation of other main menu items

 

Constants

Inserts popular constants into the section Constants

Compile

Initiates compilation of the problem

Create in another variable

Creates a connected problem in another independent variable selected by the user

Create array of  IVPs

Creates a new IVP n times larger than the original one for a set of n initial vectors specified in different manners

Graph

Opens the Graph window after successful compilation and specification of the desired trajectories

Parameters

Allows to specify:

·        a new order of differentiation other than the default;

·        another convergence radius limit;

·        to display this entire summery of all parameters.

Font

To change the font for the four edit windows

Set n-body problem

To set the Newtonian n-body problem up to 100 bodies

Help

To display help files for various topics

Demo

To run preloaded script files described in Help/Samples menu


 The four tabbed pages in the Main window

 

Equation setting

Debugging

Integration setting

Graph setting

Contains the four edit controls for entering initial value problems

Tables containing all variable and their derivatives, and the list of AD instructions for the problem

Contains all the parameters controlling the manner of integration process

Contains the table of all variables with the tools to specify the desired trajectories for plotting in the Graph window

Main window: General

Order of differentiation (default 30)

Main menu/Parameters or
hot link Order of differentiation

Convergence radius upper limit  (default 10)

Main menu/Parameters or
hot link Radius limit

Direction of the integration 

Forward/Backward radio buttons

Editing equations, initial values, parameters,  method for computing the convergence radius, opening the Polynomial Designer, creation of ODEs in another state variables, creation of an array of IVPs

Equations setting page

Specifying method of error control and error tolerances, number of elements to be stored, terminal value (if any), blind integration controls (if compiled successfully)

Integration setting page

Specifying trajectories for 2D/3D graphing (if compiled successfully)                                       

Graph setting page

Inspecting values of the variables and elements (if compiled successfully)                                      

Debugging page

Opening graph window (if compiled successfully)

Main menu/Graph

 

Main window: Equations setting page

Specifying degrees or radians (in expressions for constants or initial values) applied only in the left panes: the Constants and Initial values.

 

In the right panes only radians are in use disregarding these radio buttons!

Degrees/Radians radio buttons

Specifying how large set of variables to use for obtaining heuristic convergence radius: 

Radio buttons:

·        Main only

·        Main and auxiliary (default)

·        Main, auxiliary, and internal

         

 


Main window: Integration setting page

Quotient k=h/R  (default 0.5)

Corresponding edit control 

Method of the error control

Radio buttons

·        Middle step

·        Back step

·        No error control

Specifying relative or absolute error one by one or for a selection of cells

Radio buttons

·        One cell edit  or

·        Multi cell selection

To continue or not integration process even after maximum number of step splits the error tolerance failed

Go despite error check box

Setting an absolute and relative error tolerances

Corresponding columns in the table

To specify the Result array of elements anew and  how many elements to store      

Edit control in Results array and check box  buttons:

·        Main variables only, plus possibly…

·        Auxiliary variable also

Make Result array Circular or appendable

Check box Circular On.

If Check box Circular is Off, array Results is appendable via the button Append

To visualize the window for specifying massive integration for the predefined set of initial vectors

Check box Massive computation On

Restart blind integration from initial values

Restart button

Specifying how many steps n must be performed for every click of More button                     

Edit control in Integrate panel

Integrate n steps more

Button More

Specifying terminal value (if any)

Edit control to …

Applying terminal value

Check button if Termination is On

Making current values new initial values

Button  ¬

Placing current values into the clipboard file  

for exporting into another initial value problem

Button  ¯

Making clipboard file values new initial values

Button  ­¬

Copy the entire table into the clipboard

Button Copy to clipboard

Pasting a column of initial values from external editor or MS excel

Button Paste IVP

 


Main window: Graph setting page

Specifying curves to graph

Table "Select functions to graph"

To generate automatically all curves corresponding to variables having format x, y, x1, y1, x2, y2, …  or   x1, y1, z1, x2, y2, z2,… - in 3D

Button {x1, y1}…>>

Generating the curves according to the selection and switching to the Graph window

Button Graph

An attempt to applying previous boundaries and curves to changed equations

Button Previous

Specifying 2D or 3D graphing

Corresponding radio buttons

Specifying Red/Blue or Blue/Red glasses for 3D graphing

Click onto the glass icon

 


Main window: Debugging page

Specifying whether do display Taylor coefficients of derivatives

Radio buttons

·        Taylor coefficients

·        Derivatives

Copying the entire table into the clipboard (for Excel)

Button Copy all

What do display: either the values at the current point, or the selected analytical elements from the available

Radio buttons

·        Current values

·        Analytical elements

Visualize the Taylor profile chart for a selected function

Check box Show Taylor profile

To see the line which caused exception during compilation in the equations at the Equations page

Button Look

To display all AD instructions or only differential AD instructions

Radio buttons

·        All instructions

·        Differential instructions

 

Graph window Menu

 

File

Main window

Sizes

Switch from t to…

Swap assignment to axes

Clear

Field of directions

Parameters

Default colors

Help

 

File submenus

 

Save image

Saving one image in a selection of different formats

Save movie sequence

Saving a sequence of images for creating a movie

Load script

Loads scripts like the respective item in the Main Window

Save script

Saves scripts like the respective item in the Main Window

Print

Prints the image

Image info

Displays the technical info about the image

 

Explanation of other main menu items

 

Main window

Switches focus to the Main Window bringing it in front

Sizes

Provides a tool to quickly set the popular sizes of the graph area

Switch from t to…

Provides a tool to switch between different independent variables while integration of a set of connected problems. For example, it allows to switch from integration in respect to t into integration in respect to x, y, ….

Swap assignment to axes

Swaps assignments of particular variables to axes OX, OY, (OZ)

Clear

Clears the graph area without restarting

Field of directions

Provides a tool for plotting advance phase portraits or fields of directions for a selected pair (or triplet) of variables

Parameters

Allows to specify parameters for…

·        3D scene;

·        Bullet & curve width;

·        Density of curves;

·        Tubular plot;

·        Font for images;

·        Grid;

·        Constrains on form size;

·        Lines and solid body type;

·        Since which curve # to plot both curves and bullets (while plotting bullets only for curves prior to this #);

·        Timer type

Default colors

Resetting the default colors for curves

 

Graph window

Setting the boundaries along X , Y (and Z) axes (the 3D cage sizes)                                              

Corresponding edit controls,

then Apply button 

Quick specification of the boundaries for a few standard areas and scaling them

Menu item Size

Swapping the assignment of the curves to the coordinate axes:

X ↔ Y, X ↔ Z, or Y ↔ Z. 

Menu item Swap axes

Adjusting the boundaries to accommodate the curves after more steps of integration. (The analytic elements must be stored in Results array specified in the (Integration setting page, Main window)

Adjust button

Increasing the boundaries proportionally 1.25 times (zooming out)

Button "Zoom Out"

Decreasing the boundaries proportionally 1.25 times (zooming in)

Button "Zoom In"

Direction of integration Forward or Backward

The respective radio buttons

Resetting integration from initial values (not clearing the graph)

Restart button

Specifying how many steps n must be performed on More button click

The edit control under Integrate…

Integrate n steps more

Button More (Space bar)

"Playing" the motion whose elements were stored

Button Play

Specifying the play time (sec)

The edit control above the Play button

Perform auto integration in a given time intervals (sec) without clicking button More (or Space bar)                 

Check box Auto

Plotting trajectories as 1 pixel thin curves with no bullets                     

Check box Curves and

Radio button Thin must be checked

Plotting trajectories as thick curves

Check box Curves and

Radio button Thick must be checked

Displaying bullets     

Check box Bullets must be checked

Displaying m×n grid line on graph field

Check box Grid

Changing the number of cells in X and Y of the grid

Parameters/Grid

Drawing a field of directions for one of curves

Menu item Field of directions and  

·        Make (by default), or use

·        Phase portrait designer

To add a curve corresponding to the initial values at the mouse click

by setting these values as the new initial values, restarting,

and integrating the given number of steps forward and backward

The check box in Plotting IVP

at mouse click … must be checked.

It changes the default mouse action from dragging curves to picking the clicked coordinates as the initial values.

Calling the Switch board to switch from one independent variable

to another

Main menu item Switch from t to

Specifying bullet size (and thick curve width)

Menu item

Parameters/Bullet & curve width

Specifying curve density as distance between centers of dots on curve in pixels  0.25 to 5 (where 5 corresponds to a dotted line)

Menu item

Parameters/Curve density

 

 Graph window in 3D mode

Rotation of non-planar 3D curves

Slide controls a and b, or

the values in the table under

menu Paramters/3D scene

To control whether the rotation center is at the center of the cage or at the point (Xmin, Ymin, Zmin)

The nameless check box between the

a and b  handles: The center of the cage is anchored if the check box is checked

Axonometric view of 3D curves

Axonometric radio button

3D stereo anaglyph view

Stereo radio button

Visualize 3D cage of the parallelepiped or the Axes

Cage On check box

Axes On check box

Display curves as tubular graphics

Tube On check box

Adjusting parameters of stereo viewing

The table under menu

Parameters/3D scene