CompuServe Thread

Someone just asked me: < What references can I find for more information on the algorithm for your particle system? >. Thought some of you might also like to know. The animations I've uploaded, created with my particle system, were the result of equations not discussed in references. I intended to use gravity but made errors, found by Dennis Conklin, in the derivation. (I will soon distribute updated code that incorporates both the current equations, and those for gravity.) I did not find information (in Endicott, NY) on programming particle systems. Eventually I went back to basics and worked with Newton's Second law. You can find material on that subject in any College Physics book. The books I used (from my college days in the 60s) were: [1] University Physics, F. W. Sears and M. W. Zemansky [2] College Physics, by R. L. Weber, K.V. Mannig and M. W. White [3] Elements of Physics, by Shortley and Willians I programmed the equations in a straightforward way, in a "time" loop where acceleration, velocity and position are repeatedly updated. I used assumptions justified in an article in Scientific American about modeling galaxies. The assumptions were that the mass for a galaxy could be treated as concentrated at a point, and that the particles (the stars) themselves generated no gravity field, but were affected by it. And, there is no need to check for collisions. Anyhow, Newton proved that the mass of a sphere can be treated as being concentrated at one point (e.g., we fall toward the center of the earth). I looked at a lot of other books, but found little specific help for developers of particle systems. But, you might be interested anyway, so here's a summary. There is a (small) amount of material on the use of the Fast Fourier Transform to solve Poisson's equation for a gravitational field in: [4] Numerical Recipes in C, the Art of Scientific Computing, by W. H. Press, S. A. Teukolsky, W. T. Vettrling and B. P. Flannery (in HEAT24.ZIP I did something similar using EXCEL instead of C). I like the style used in this book for C-programs, and will follow some of the examples in my work. For an update on Gravity (nice reading material), but probably only available from Scientific American: [4] A Journey into Gravity and Spacetime by J. A. Wheeler For background (in laymen's terms) of why we can't … [4] Newton's Clock, Chaos in the Solar System, by I. Peterson "a solitary planet residing in solar system dominated by two stars of equal mass would follow an extremely complicated, practically unpredictable orbit." If not convinced, and if you are (very) mathematically-inclined, glance at the chapter on "The Two-Body Central Force Problem" in [5] Classical Mechanics, by H. Goldstein "not all two-body motion problems are integrable in terms of well-known functions." This book also contains detailed mathematical analysis on orbit equations, scattering of particles, inertia tensors, coriolis force, etc. The following books are a little easier to read: [6] Theoretical Mechanics, An Introduction to Mathematical Physics, by H. Goldstein [7] Methods of Mathematical Physics, by Courant and Hilbert (1953) But, you might want to have nearby the handy $12.50 [8] Dictionary of Physics (from Penguin books) Most of the data for the solar system came from the Encyclopedia Britannica (where miles, kilometers, or astronomical units, are randomly used). Ed K