Playing with the
DEMO
This
is a limited version of the
To install the program, just unzip it into an empty folder of your choice. Then run TCenter.exe and follow through multiple examples producing 2D trajectories (on the white background) and 3D (on the black background requiring Red/Blue glasses).
Generally, when clicking the samples under Demo menu item, the program
automatically loads and displays the curves of the chosen problem in
the Graph window. Then you can click the Play button to replay the
motion in the real time. Playing in the real time visualizes the
important physical and mathematical properties of the problems. For
example, in the Lagrange case of the three body problem (Demo/3 bodies/Lagrange case) you
can observe the motion along ellipses with
acceleration and deceleration by the Kepler law.
Or in the case for the double spiral (Demo/Spirals/Double) you can
notice that it takes the same time for the bullet to make every lap
disregarding its size (for which there exists mathematical proof).
You can view the ODEs
of the respective problem in the Main window in the first of its four
pages: the page "Equations". It may be helpful to keep Main and Graph
windows at separate monitors, and to resize the
Graph window for bigger dimensions.
Rushing to experience
the 3D stereo viewing, begin with the famous objects like Möbius
strip, Klein bottle, or Linked tori outlines.
However physically the examples in celestial mechanics are the most
telling. In
the start menu select Demo/Three
Bodies/Disturbed/3D. Now put on your Red/Blue
glasses
(over those you usually use) and get ready for fun.
What
you hopefully see looks like a "fishing line" hanging in thin
air between the monitor and your face. These are trajectories of three
bodies
moving under gravitational pull. More specifically, this is the so
called
disturbed Lagrange case. (In the Lagrange case proper, three equal
masses are
placed at vertices of an equilateral triangle with initial velocities
comprising an equilateral triangle co-planar to the first one). Click
the Play button. This initiates the real
time animated 3D stereo motion of the bullets representing the three
bodies
with all the accelerations, decelerations, and couplings.
When
they come to rest, you may try exploring the elements of the
trajectories with
a "tactile" 3D cursor. Move it into the scene, where it will
take form of a small cross. The mouse motion always moves the stereo
cursor
in a
plane parallel to the screen. In order to control its depth, use the
mouse wheel. The current 3D coordinates of the moving cursor always
appear at
the top
window panel.
Now, applying the 3D
control, try to touch
one of
the trajectories in space with the 3D cursor. If the speakers are ON,
you will
hear a clicking sound when the touch occurs: this is the so called
"tactile"
audio feedback, helping to explore points of interest in the curves in
3D.
You
can rotate the curves in the space with the Turn controls, and view
them conventionally as isometric (without Red/Blue glasses). You can
also plot the curves in the tubular graphic achieving the proper skew
resolution.
For
the full list and brief explanation of over the 70 pre-loaded samples
see the file Samples.
To
obtain the full version of
the