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Central Force Integrator (CFI) Help File

  • HELP. Displays this help screen. To exit, click one of the "Exit Help" buttons located at the top and bottom of this screen.

    Radial Force Equation:

    This program solves the differential equation d2r/dt2 = -f(r) (r/r) where f(r) = (Arm + Brn) is an inwardly directed force. You can control the force law by choosing the four constants A, m, B, and n. Here are some examples to try:

  • Choose A=1, m=-2, B=0, n=0 for gravity.
  • Choose A=1, m=1, B=0, n=0 for a spring (Hooke's Law).
  • Choose A=1, m=-2, B=0.001, n=-4 to simulate the effects of General Relativity (in reality, B would be much much smaller).
  • Choose A=1, m=-3, B=0, n=0 for Cotes' Spirals. See what happens for the purely azimuthal velocities Vθ = 0.99 and Vθ = 1.01. Try Vθ = 0.999.

    Initial Conditions:

  • The RADIUS, r, is the initial distance between the origin and the particle's position.
  • The RADIAL VELOCITY, Vr, is the rate at which the radius, r, is changing its length. Velocities are given in units of the circular speed.
  • The AZIMUTHAL VELOCITY, Vθ, is the rate at which the radius, r, is changing direction. Velocities are given in units of the circular speed (so Vr = 0 and Vθ = 1 results in an initially circular orbit.

    Approximate Number of Orbits:

  • This entry determines the length of the orbital integration; more precisely, it is the number of orbits that the particle would complete if it were following a circular path. Try small numbers first to cut down your wait time.
  • SUBMIT FORM. Send the parameters that you have chosen to the orbital integration program!
  • LOAD DEFAULTS. Set all parameters back to their default values.
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