Initial position x(0) = Initial position y(0) = Initial momentum px(0) = Initial momentum py(0) = Initial momentum p(0) = Initial momentum φ(0) = Mass 1 = Initial position x2(0) = Initial position y2(0) = Initial momentum px2(0) = Initial momentum py2(0) = Initial momentum p2(0) = Initial momentum φ2(0) = Mass 2 = Terminal time t(off) = Maximum step size dt = Start launch angle phi1 = Start launch angle phi2 = Number of burst paths = Charge of Nucleus 1 = x-Position of Nucleus 1 = y-Position of Nucleus 1 = Charge of Nucleus 2 = x-Position of Nucleus 2 = y-Position of Nucleus 2 = Coulomb (k12) = Core thickness r = x-Stark field Ex = y-Stark field Ey = Zeeman field Bz = Diamagnetic strength k = Plank constant h-bar = Color quantization hues = Color quantization bands = Fractional Error (e-x), x = Particle Size = Control's Zoom =
 Fix r(0) Fix p(0) Do swarm Beam
 Plot r(t) Plot p(t) P-factor =
 No stops Field vectors Info Draw masses Axes Coordinates Lenz Set p by φ Elastic Set CM 2 Free Color quantized reduced action Reduced action front Save to GIF
 Chapter 1 Orbit Families and Action            Families of particle orbits are drawn in a varying color which represents the classical action or Hamiltoon's characteristic function SH = ∫p dq.(Sometimes SH is called 'reduced action'. ) The color is chosen by first calculating c = SH modulo h-bar (You can change Planck's constant from its default value h/2π = 1.0) The chromatic value c assigns the hue by its position on the color wheel (e.g.; c=0 is red, c=0.2 is a yellow, c=0.5 is a green, etc.). Chapter 2 Rutherford Scattering            A parallel beam of iso-energetic alpha particles undergo Rutherford scattering from a coulomb field of a nucleus as calculated in these demos. It is also the ideal pattern of paths followed by intergalactic hydrogen in perturbed by the solar wind. Chapter 3 Coulomb Field (H atom)            Orbits in an attractive Coulomb field are calculated here. You may select the initial position (x(0),y(0)) by moving the mouse to a desired launch point, and then select the initial momentum (px(0), py(0)) by pressing the mouse button and dragging. Chapter 4 Molecular Ion Orbits            Orbits around two fixed nuclei are calculated here. A set of elliptic coordinates are drawn in the background. After running a few trajectories you may notice that their caustics conform to one or two of the elliptic coordinate lines.