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HELP - Model Sim Using Square Law

Posted: Tue Jul 23, 2019 10:57 am
by extendnovice
Setting: Battle of Little Bighorn
Assumptions: Consider the 7th Cavalry (B) and the Sioux forces (R) to be homogenous cavalry forces - initial strengths as given in the article: Custer had 675 men, and there were 5,000 Sioux warriors. Assume the battle follows the Lanchester square law without reinforcement, given by:

(1.2) dB/dt=-aR(t)
dR/dt=-bB(t)

Assume that the ratio of b/a is 3.0, and let a = .01. Initially, both a and b are constant with respect to time and history informs us that the battle period was on the order of no more than several hours. Model the battle in ExtendSim using Equations (1.2), and for a scenario where all of the 7th Cavalry attacks all of the Sioux at once (this does not match accounts in the historical record), determine this battle outcome. How long until one side is annihilated, and what are the ending strengths?