Orbimania simulates the N-body problem in 2 dimensions with inverse-square forces. The remarkable feature of Orbimania is its fast graphics -- it displays the potential field in real time. Even non-technical users may find it interesting to play with the images of the potential field. Furthermore, the graphical user interface allows you to twiddle physical parameters without entering numbers. Even children may find Orbimania amusing without understanding the physics.
System Requirements: Orbimania requires a PowerPC Macintosh with System 7 and at least 256 colors. It works best with 16-bit color ("thousands of colors").
Demo: Go to the folder "Examples" and click on the file named Positronium. When the Orbimania window comes up, go to the window beside it with the red STOP sign and click on the STOP sign. The sign will toggle to a green GO and start the simulation.
Learning More About Orbimania
The best way to learn about Orbimania is to experiment with it. To learn about a button or icon, hold the cursor over the item and press H . A window explaining the feature should pop up. The buttons and icons allow you to create/erase particles, and let you to set the following physical parameters:
Position
Velocity
Mass
Charge
Direction of time
Sign of force law (opposites attract or opposites repel)
You can zoom and reposition the view of the Orbimania universe. You can choose whether to display the particle's futures, masses, or velocity vectors.
Buzzwords: Orbimania models arbitrary inverse-square problems. However, for uniformity, the documentation uses electrostatic terms. A particle's charge generates its potential. The potential field is the sum of all particle potentials. The force on a particle is proportional to its charge times the gradient of the potential field. A particle's mass resists the force according to the law force=mass*acceleration.
Force laws: To model electrostatics, set the force law to "opposites attract".
To model gravity, set the force law to "opposites repel" and check the "gravity" box.
In gravity mode, the absolute value of the charge/mass ratio is constant, so that the "charge" models gravitational potential.
Examples
The following examples are in the folder "examples".
Acceleron: Shows a positive mass chasing a negative mass. The pair of particles accelerate forever! They do not violate conservation laws, because the net mass of the system is zero! You can buy negative masses at upscale hardware stores that sell frictionless incline planes and massless pulleys.
Mass Spectrometer: Models an (electrostatic) mass spectrometer of sorts. The model consists of five particles. Two massive particles with opposite charges form the spectrometer. The three other particles (coming in from the left) are the samples to be weighed. The three samples have approximately the same charge, but differ in weight. The higher the charge/mass ratio, the more the sample is deflected. Can you tell which samples have the lowest and highest mass? Clicking on the "future" box may help. Check your answer by rerunning the simulation with the "mass" box checked.
Positronium: Positive and negative charge orbit each other. This models the "element" positronium, which consists of an electron and positron (anti-electron) orbiting each other.
Quadrupole: Four charges implode.
Ternary Star: Models a ternary star. Ternary stars are popular in science fiction, but the model makes it clear why you do not want to live near one.
About the Programming
Mathematics: Unlike some N-body simulations, Orbimania usually preserves energy, linear momentum, angular momentum, and symmetry under time reversal up to round-off error. This is possible because Orbimania uses a covariant finite-difference method developed by Donald Greenspan [1]. Unfortunately, the method is implicit and requires root finding. The author employs a rinky-dink fixed-point solver that occasionally fails. When it does, the conservation/symmetry laws are broken. This happens when two bodies come very close together and each time step drastically changes their relative positions. Eventually, the author may find time to implement Newton's (multivariate) method as recommended by Greenspan's paper.
The finite-difference equations do not preserve periodicity of orbits.
Code: Orbimania generates optimized pipelined code on the fly. This is essential to obtaining maximum speed from the PowerPC chip. Some people pontificate that self-modifying code is a rehensible programming practice that should be banned. However, the author is a professional compiler writer and thus carries diplomatic immunity in this matter.
Known Problems:
* Does not suspend/resume cleanly.
* Root finder is fixed-point method. Should be replaced by Newton's method.
* Limited to 8 particles.
* Orbimania window turns completely yellow on occasion.
To Reach The Author:
The author welcomes comments, and can be reached at:
1406 Country Lake Dr.
Champaign IL 61821
robison@kai.com
Legal
Distribution:
Orbimania 1.0 is freeware. This software may be freely distributed as long as said software and this "README" file are not modified and both are distributed together.
Disclaimer:
The author, Arch D. Robison, assumes no responsibility with regard to use of this software. Use this software at your own risk. This software has no warrantee, expressed or implied. The author is not responsible for any liability, direct or indirect, that may arise from the use of this software.
Orbimania does not duplicate the real world. Orbimania does not model relativistic or quantum effects. Large scale curvature and short scale breakdown of space-time is not modeled. Orbimania employs arithmetic with finite range and precision. Orbimania's world is flat. Orbimania is strictly for amusement and qualitative understanding of N-body problems. It is not suitable for serious engineering calculations such as (but not limited to) interplanetary travel or particle accelerators.
Bibliography
[1] D. Greenspan, "Completely Conservative, Covariant Numerical Methodology,"
Computers Math. Applic., Vol. 29, No. 4, pp. 37-43, 1995.
[2] So you really read all this! Here's an otherwise undocumented feature:
Press ] to double the length of the "future" dot track. [ halves it.
You can double it up to 256 dots per track (default is 32 dots per track).
