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 the steps guiding you through several
examples producing
3D trajectories.
In
the start menu select Demo/Three
Bodies/Disturbed/3D: it opens the initial value problem script and
compiles
it. After clicking OK to the message "Compilation successful", some
knotty Red and Blue curves will appear. Now put on your anaglyphic
glasses
(over those you usually use, if any) and get ready for fun. (It's
recommended
to maximize the Graph window).
What
you hopefully perceive 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 – Demo/Three Bodies/ Symmetrical). This "fishing
line" is a result of a small disturbances applied perpendicularly to
the
initial plane (the plane of your screen).
The
program is capable of producing something more than "still life". Click
the Play button. This initiates 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
transform into a small cross. The mouse always moves the stereo cursor
in a
plane parallel to the screen. In order to control its depth, use the
mouse wheel. Another method of changing the depth is
to move
the mouse keeping depressed either Ctrl
key (to bring the cursor closer to
your eyes), or Shift key (to move it
away from you). Current 3D coordinates of the 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.
You
can rotate the curves in the space with the Turn controls. With the
given
specific sizes of the parallelepiped, you may notice that the front
side
(controlled by Max Z value) keeps the curves inside the parallelepiped
"flattening"
them. (Therefore increase Max Z).
Already
familiarized with the 3D stereo features of the package, you may try
several
other problems. Click Main Panel in the menu to re-visualize the main
form, and
go to Demo/Four Bodies. The two pairs
of bodies with equal masses are all initially placed in a horizontal
plane,
parallel to your desk (perpendicular to the screen). The horizontal
components
of the velocities provide near circular motion for each coupled pair,
while the
small vertical components push the two pairs into a large circular
motion
around the center of the masses (see the initial values in the Main
window). At
the beginning the trajectories spin into a braid looking like a torus
(and like
the tiny braided rings of Saturn shot by the Voyager probe), but the
braid
actually does not outline a torus: you can notice that both coupled
pairs
preserve their initially horizontal plane.
Another
fascinating example of 3D motion is under Demo/Möbius.
You can watch 4 bullets lined up in a straight line whose motion
outline a
Möbius surface winded 1.5. To get a more common one (winded 0.5),
change value of
n=0.5 (in Constants), Compile, click
button Previous (in Graph setting
page), click Clear in Graph window,
and finally click the More button.
You
can explore several more 3D stereo examples opening them as scripts.
Click the Main Panel and go to File/Open
script menu item. Here are
files producing 3D stereo images:
PendulumApple.scr,
PendulumFlower.scr (spherical pendulum)
KnotChain3D.scr,
TrefoilKnot3D.scr
MobiusLarge.scr
Beside
3D stereo samples, there
are also instructive examples in 2D, such as the recently discovered
eight-shaped
solution of the three body problem called "Choreography" (Demo/Three
Bodies/Choreography). Under File/Open script there
are also two more
classical examples in celestial mechanics: the Euler case with the
bodies of
equal masses (3EqBodEuler.scr) and the case when one mass is near zero
(3NonEqBodEuler.scr).
There are also scripts for single and double pendulums, and the Four
body
Lagrange case as well.
To
obtain the full version of
the