Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Welfare
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Authors
Brown, Gerald G.
Taylor, James G.
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1976
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(Received original October 17, 1974; final, May 12, 1975)
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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.
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Article
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Operations Research, 24, pp. 44-69.
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Operations Research (OR)
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Citation
Brown, G.G. and Taylor, J., 1976, “Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Welfare,” Operations Research, 24, pp. 44-69.
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defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.