Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Welfare
Abstract
This paper develops a mathematical theory for solving deterministic, Lanchester-type, 'square-law' attrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It gives a general form for expressing the solution of such variable-coefficient combat attrition equations in terms of Lanchester functions, which are introduced here and can be readily tabulated. Different Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. We give results for two such forms: (1) effectiveness of each side's fire proportional to a power of time, and (2) effectiveness of each side's fire linear with time but with a nonconstant ratio of attrition-rate coefficients. Previous results in the literature for a nonconstant ratio of these attrition-rate coefficients only took a convenient form under rather restrictive conditions.
Description
Operations Research, 24, pp. 44-69.
Rights
defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
Related items
Showing items related by title, author, creator and subject.
-
Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Warfare
Taylor, James G.; Brown, Gerald G. (1976-01);This paper develops a mathematical theory for solving deterministic, Lanchester-type, 'square-law' attrition equations for combat between two homogeneous forces with temporal variations in fire effec- tivenesses (as expressed ... -
Application of differential games to problems of military conflict: Tactical allocation problems, Part II
Taylor, James G. (Monterey, California. Naval Postgraduate School, 1972-11); NPS55TW72111AThe mathematical theory of optimal control/differential games is used to study the structure of optimal allocation policies for some tactical allocation problems with combat described by Lanchester-type equations of warfare. ... -
Application of differential games to problems of military conflict: Tactical allocation problems, Part I
Taylor, James G. (Monterey, California. Naval Postgraduate School, 1970-06-19); NPS-55TW70062AThe mathematical theory of deterministic optimal control/differential games is applied to the study of some tactical allocation problems for combat described by Lanchester-type equations of warfare. A solution procedure is ...