APPLICATION OF LANCHESTER'S MATHEMATICAL LAWS IN MILITARY STRATEGY

Abstract

Mathematics, as the science of numbers, structures, and models, plays an important role in many aspects of military operations and strategies. From calculating the probability of success or failure of military operations to determining the best ways to deploy troops and resources, mathematics provides military strategists with powerful tools to make informed and effective decisions. One of the most important aspects of using mathematics in the military is developing strategies for combat operations. From determining the location of troops and the size of forces to the conditions of operations, mathematical methods and models help to optimize decisions. To determine the probability of success of military operations, mathematics uses probability theory and statistics. This allows us to estimate the probability of achieving the goal, taking into account various factors such as military equipment, enemy location, and other external conditions. The analysis of previous military conflicts and data allows us to statistically estimate probability distributions and predict military events. Mathematics also plays an important role in solving logistics and resource allocation problems. Determining the optimal route for the movement of troops and resources can be formulated as a path optimization problem. Mathematical methods are also used in the field of intelligence and the development of new technologies. Cryptography, which protects important information from unauthorized access, is based on complex mathematical algorithms. Mathematical models can also be used to simulate military operations, study the impact of new weapons systems, or analyze missile trajectories. It is worth adding that mathematical laws help to analyze and predict the outcomes of military conflicts, in particular, to determine the impact of the size and effectiveness of the enemy forces on the probability of success. In this article, the main focus is on the laws of Lanchester's mathematical models. The article presents the derivation of Lanchester's linear law and an example of its application. The mathematical principles of the quadratic Lanchester's law are considered on an example. It is indicated and highlighted how these mathematical laws can be applied in the context of the Russian-Ukrainian conflict.