Accession Number:

ADA063173

Title:

On Liouville's Normal Form for Lanchester-Type Equations of Modern Warfare with Variable Coefficients.

Descriptive Note:

Technical rept.,

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s):

Report Date:

1978-09-01

Pagination or Media Count:

40.0

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 Liouvilles 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 battles outcome without explicitly solving the deterministic combat equations and computing force-level trajectories are developed for fixed-force-ratio-breakpoint battles by considering Liouvilles 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. Liouvilles normal form is also shown to yield an approximation to the force-level trajectories in terms of elementary functions. Author

Subject Categories:

  • Operations Research
  • Military Operations, Strategy and Tactics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE