# Killeen's Mechanics (minor improvement)

[From Bruce Abbott (960106.1425 EST)]

I just realized that I could have done a little better job of presenting the
equivalent formulas for Killeen's model in lines 5 and 6 of my table, which
will bring out the parallel with the control model even more strongly. On
line 5, make the following substitution:

change g = v*h/s to g = v*Y/s

This makes g a constant, as in the control model. On line 6,

change B = g*R to B = g*e*R,

which compares to B = g*e for the control model. The table will look like
this after the changes:

Control model Killeen's model Equivalent formula

···

-----------------------------------------------------------------------
(1) F = F + (m*R - M)*dt d = d + (M - m*R)*dt F = F + (m*R - M)*dt

(2) p = F p = F

(3) e = Fr - p e = Fr - p

(4) h = Y*d h = Y*e

(5) g = constant a = v*h g = v*Y/s

(6) B = g*e B = a*R/s B = g*e*R

(7) R = B/n R = B/n R = B/n
-----------------------------------------------------
The "equivalent equations" on lines 5 and 6 are not strictly equivalent to
Killeen's on lines 5 and 6, but their combined effects are mathematically
equivalent.

Regards,

Bruce