Force-Annihilation Conditions for Variable-Coefficient Lanchester-Type Equations of Modern Waxfare
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Authors
Taylor, James G.
Comstock, Craig
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1977
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1977
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Abstract
This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” dttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as ex- pressed 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 erponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results pro- vide 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 hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponentid-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients.Thistheory is applied to general power attrition-rate coefficients: exact force-annihilation mults are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter areobtained when the offset parameter ispasitive.
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Article
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Naval Postgraduate School
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This research was supported by the Office of Naval Research as part of the Foundation Research Program at the Naval Postgraduate School
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Taylor, James G., and Craig Comstock. "Force‐annihilation conditions for variable‐coefficient lanchester‐type equations of modern warfare." Naval Research Logistics Quarterly 24.2 (1977): 349-371.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.