On Liouville's normal form for Lanchester-type equations of modern warfare with variable coefficients
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Authors
Taylor, James G.
Subjects
Lanchester Theory of Combat
Combat Modelling
Attrition Modelling
Combat Dynamics
Deterministic Combat Attrition Battle-Outcome Prediction
Combat Modelling
Attrition Modelling
Combat Dynamics
Deterministic Combat Attrition Battle-Outcome Prediction
Advisors
Date of Issue
1978-09
Date
1978-09
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
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
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS55-78-024
Sponsors
supported jointly by Naval Analysis Programs (Code 431),
Office of Naval Research and by the Foundation Research Program of the Naval
Postgraduate School with funds provided by the Chief of Naval Research
Funder
N0001478WR80023
Format
Citation
Distribution Statement
Rights
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.