Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare, I
Subtitle: mathematical theory
By: by James G. Taylor and Craig Comstock
Contributors: Comstock, Craig; Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1976
Place of publication: Monterey, Calif
Language: eng
Number of pages: 38
Subjects: Mathematical models; Tactics; Combat; Differential games
Description: This paper develops a mathematical theory of predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type "square-law" attrition equations for combat between two homogeneous forces with temporal variations in fire effectiveness (as expressed by the Lanchester attrition-rate coefficients).  It introduces a canonical auxiliary parity-condition problem for the determination of a single parity -condition parameter ("the enemy force equivalent of a friendly force of unit strength") and new exponential-like general Lanchester functions.   Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of tow Lanchester functions.  These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hperbolic-like general Lancehster functions.  Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rat coefficients.  This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero, while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive. (Author)
Notes: Title from cover.

"Prepared for: Office of Naval Research, Arlington, Virginia 22217"--Cover.

"Partial Report for Period April 1976 - July 1976"--Cover.

"NPS-55Tw76081"--Cover.

Author(s) subject terms: Lanchester theory of combat, combat dynamics, deterministic combat attrition.

Includes bibliographical references (p. 34-35).

"Approved for public release; distribution unlimited"--Cover.

Technical report; August 1976.