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 =
P-factor =
Color quantized
reduced action
Full orbit on UI
COM Symbols
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.