A mathematical theory for variable-coefficient Lanchester-type equations of 'modern warfare'
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Authors
Taylor, James G.
Brown, Gerald G.
Subjects
Lanchester Theory of Combat
Combat Dynamics
Deterministic Combat Attrition
Combat Dynamics
Deterministic Combat Attrition
Advisors
Date of Issue
1974-11
Date
Publisher
Monterey, CA; Naval Postgraduate School
Language
Abstract
A mathematical theory is developed for the analytic solution to deterministic Lanchester-type "square-law" attrition equations for combat between two homogeneous forces with temporal variations in system effectiveness (as expressed by the Lanchester attrition-rate coefficient). Particular attention is given to solution in terms of tabulated functions. For this purpose Lanchester functions are Introduced and their mathematical properties that facilitate solution given. The above theory is applied to the following cases: (1) lethality of each side's fire proportional to a power of time, and (2) lethality of each side's fire linear with time but a nonconstant ratio of these. By considering the force-ratio equation, the classical Lanchester square law is generalized to variable-coefficient cases in which it provides a "local" condition of "winning."
Type
Technical Report
Description
Series/Report No
Department
Operations Research and Administrative Sciences
Organization
Identifiers
NPS Report Number
NPS55TW74111
Sponsors
Prepared for: Office of Naval Research, Arlington, Virginia
Funding
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.