This paper is devoted to the research of hydrodynamic processes by the motion of bodies in a fluid. As an example of such researches are testing ship models at the design of a new full-scale ship. The aim was to develop a three-coordinate theory similarity with independent geometric and kinematic (speed) scales for each of the coordinates. In this case, the geometric scales for the model and full-scale object (equation), (equation) and (equation) at the length L, the width B and the draft T will be different: nL ≠ nB ≠ nT. The kinematic (speed) scales (equation), (equation) and (equation) for coordinate x, y and z also will be different: nvx ≠ nvy ≠ nvz.

This approach allows us to recalculate the results of model tests to a full-scale object, which don't have a full geometric and kinematic similarity. However, the condition remains that the models and the full-scale object are alike by form and motion.

The purpose of this paper is to construct a mathematical model of the theory of similarity to formally dissimilar, but alike ("likeness") bodies. Ellipsoidal models with different sizes and scales are chosen as an object of researches. This is due to the fact that for an ellipsoid it is possible to have a precise mathematical description of the surface. Therefore, all the mathematical procedures are accurate for this body. In this case it is possible to have a precise mathematical description of the theoretical results.

The authors have special machines available for manufacturing high-precision models of any shape for experimental studies in a towing tank. The experimental results were compared with the theoretical results. At the same time, calculation was made of the model test results to full-scale object.

Based on theoretical and experimental studies, the authors developed a three-coordinate similarity theory for bodies that don't have a strict similarity, but have the condition of likeness.

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