On Liouville's normal form for Lanchester-type equations of modern warfare with variable coefficients
By: by James G. Taylor
Contributors: Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1978
Place of publication: Monterey, California
Language: eng
Number of pages: 34
Subjects: Differential equations; Mathematical models; Fire control (Gunnery); Military art and science; Combat
Description: 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.
Notes: Title from cover.

"NPS55-78-024"--Cover.

"September 1978"--Cover.

"Prepared for: Office of Naval Research, Arlington, VA 22217."

Includes bibliographical references (p. 29-32).

"Approved for public release; distribution is unlimited"--Cover.

Technical report; 1978.

ck/ 7/15/09.