Force-Annihilation Conditions for Variable-Coefficient Lanchester-Type Equations of Modern Waxfare
Taylor, James G.
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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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Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare, I: Mathematical Theory Taylor, James G.; Comstock, Craig (Monterey, California. Naval Postgraduate School, 1976); NPS-55Tw76081This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type "square-law" attrition equations for ...
Force‐annihilation conditions for variable‐coefficient Lanchester‐type equations of modern warfare Taylor, James G.; Comstock, Craig (Wiley Online, 1977-06);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” áttrition equations ...
Numerical Determination of the Parity-Condition Parameter for Lanchester-Type Equations of Modern Warfare Brown, Gerald G.; Taylor, James G. (1978);This paper presents a simple numerical procedure for determining the parity-condition parameter for deterministic Lanchester-type combat between two homogeneous forces. Deterministic dierentidequation combat models are ...