Playing with the
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.
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
the full list and brief explanation of over the 70 pre-loaded samples
see the file Samples.
obtain the full version of