Soliton

Example of use of [Active Axes], [Line-Coordinate] and [Motor]. In this example we construct the graph of the function y = A/(1+(B-x)^2), using the tool [Measures\Line-Coordinate _ _ ], the tool [Geometric-Locus] (4th button from below) and the possibility (new since version 1.4.1) of [Dynamic Axes]. These are defined by de-pressing the button

on the right toolbar, while holding down simultaneously the CTRL key. In addition we construct the mechanism to vary parameter B and create the impression of a soliton.

1) Having constructed the coordinate axes, by the actions described above,
2) Put a point X on the x-axis, using the [Point-tool] (third button) and clicking near the x-axis, while pressing the SHIFT button.
3) Select the tool [Measures \ Line-Coordinate _ _] and a) click on the x-axis, b) click on point X. This constructs the label [x = ...] displaying the coordinate of X.
4) Somewhere in the white space type the text 7.6
5) While this text box is selected press the key Enter. This creates the corresponding number-object [7.3], playing the role of parameter A.
6) Set a point C on the x-axis and create a moving point B on the x-axis, starting at C. For this set C on the axis (as in 2) and create a new motor (fourth item from below of submenu of fourth button from below). Then right click on the created motor-tag and select the item [Moving]. Then click first at C and the at the motor.
7) Select the tool [Measures \ Line-Coordinate _ _] and a) click on the x-axis, b) click on point B. This constructs the label [B = ...] displaying the coordinate of B.
8) Somewhere in the white space type the text: formula y = A/(1+(x-B)^2)
9) Press the key [ESC] (escape). This creates the corresponding formula-object (that with the blue box).
10) Right click on the formula object and select the menu-item [Activate].
11) Then click on labels [A= ... ] , [x = ...] and [B= ...]. This produces the label [y = ... ].
12) Double click on label [y = ... ] holding down the key F4. This defines point Y on y-axis, representing the value of label [y = ... ].
13) Select the tool [Quadrangles \ Screen-Rectagle]. Click on Y ...drag ... release at X. This defines the rectangle with diagonal YX.
14) Select again the point-tool and put point E on the upper-right corner of the screen rectangle.
15) Select the tool of [Geometric-Locus] (4th button from below). Click on X and then click on E. This produces the graph of the function.
To see the animation press the green button of the motor. Look at the file SolitonInterference.html for a similar example.

http://users.math.uoc.gr/~pamfilos/