On Liouville's normal form for Lanchester-type equations of modern warfare with variable coefficients
Taylor, James G.
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This paper shows that much new information about the dynamics of combat between two homogeneous forces modelled by Lanchester-type equations of modern warfare (also frequently referred to as 'square-law' attrition equations) with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients) may be obtained by considering Liouville's normal form for the X and Y force-level equations. It is shown that the relative fire effectiveness of the two combatants and the intensity of combat are two key parameters determining the course of such Lanchester-type combat. New victory-prediction conditions that allow one to forecast the battle's outcome without explicitly solving the deterministic combat equations and computing force-level trajectories are developed for fixed-force-ratio-breakpoint battles by considering Liouville's normal form. These general results are applied to two special cases of combat modelled with general power attrition-rate coefficients. A refinement of a previously know victory-prediction condition is given. Temporal variations in relative fire effectiveness play a central role in these victory-prediction results. Liouville's normal form is also shown to yield an approximation to the force-level trajectories in terms of elementary functions
NPS Report NumberNPS55-78-024
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Further canonical methods in the solution of variable-coefficient Lanchester-type equations of modern warfare Taylor, James G.; Brown, Gerald G. (Monterey, California. Naval Postgraduate School, 1977-06); NPS55-77-27This paper introduces an important new canonical set of functions for solving Lanchester-type equations of modern warfare for combat between two homogeneous forces with power attrition-rate coefficients with "no effect." ...
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