Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare, I: Mathematical Theory
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" 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 cannonical 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 two 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 hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate 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.
NPS Report NumberNPS-55Tw76081
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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 ...
Numerical determination of the parity-condition parameter for Lanchester-type equations of modern warfare Taylor, James G.; Brown, Gerald Gerard (Monterey, California. Naval Postgraduate School, 1977-03); NPS55-77-10This paper presents a simple numerical procedure for determining the parity-condition parameter for Lanchester-type combat between two homogeneous forces. The combat studied is modeled by Lanchester-type equations of modern ...
Taylor, James G.; Brown, Gerald G. (Monterey, California. Naval Postgraduate School, 1974-11); NPS55TW74111A mathematical theory is developed for the analytic solution to deterministic Lanchester-type "square-law" attrition equations for combat between two homogeneous forces with temporal variations in system effectiveness (as ...