History of Science and Engineering Annotation << Back VECTOR CALCULUS IN SOMOV’S MECHANICS A.O. Yulina In mathematics, the concept of a vector was introduced by W. Hamilton. In mechanics, Hamilton determines the hodograph of the radius vector of the point to set the trajectory of the point. Hamilton describes the spatial interpretation of the rotational motion of a rigid body relative to a fixed point by vectors, which are a special kind of hypercomplex numbers, which he calls quaternions. In his fundamental works on the theory of quaternions, Hamilton sets out the basics of vector algebra and vector analysis, formulates the laws of geometric addition, subtraction, multiplication, considers two types of products of vectors – scalar and vector. He also owns the operations of differentiation and integration of vectors. However, Hamilton’s brilliant ideas did not soon find recognition in France, Germany and Russia. As can be seen from the above, the 19th century was marked by the rapid development of both theoretical and applied mechanics: many works appeared on the mechanics of motion and the corresponding mathematical tools. This was due to the industrial revolution and new military demands at the beginning of the 18th century. Thus, the range of brilliant ideas and new problems faced by O.I. Somov was incredibly large. The central merit of Somov was the introduction to the mechanics of vector calculus. Somov deeply studied the works of Hamilton and took from them the most necessary and useful for the presentation of mechanics at a fundamentally new level. Keywords: Vector calculus, Hamilton, Somov. DOI: 10.25791/intstg.3.2023.1407 Pp. 26-33.