A mathematical theory for variable-coefficient Lanchester-type equations of 'modern warfare'
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."
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.NPS Report Number
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