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dc.contributor.authorTaylor, James G.
dc.date1978-09
dc.date.accessioned2013-02-27T23:37:35Z
dc.date.available2013-02-27T23:37:35Z
dc.date.issued1978-09
dc.identifier.urihttp://hdl.handle.net/10945/29432
dc.description.abstractThis 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 functionsen_US
dc.description.sponsorshipsupported 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 Researchen_US
dc.description.urihttp://archive.org/details/onliouvillesnorm00tayl
dc.language.isoen_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis 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.en_US
dc.subject.lcshVORTEX-MOTION.REYNOLDS NUMBER.HYDRODYNAMICS.FLUID DYNAMICS.en_US
dc.titleOn Liouville's normal form for Lanchester-type equations of modern warfare with variable coefficientsen_US
dc.typeTechnical Reporten_US
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.subject.authorLanchester Theory of Combaten_US
dc.subject.authorCombat Modellingen_US
dc.subject.authorAttrition Modellingen_US
dc.subject.authorCombat Dynamicsen_US
dc.subject.authorDeterministic Combat Attrition Battle-Outcome Predictionen_US
dc.description.funderN0001478WR80023en_US
dc.identifier.npsreportNPS55-78-024


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