### Vector functions of a scalar argument in research of point and solid body kinematics

O. A. Gulivets, S. Yu. Oliinyk, G. A. Markevych

#### Abstract

In the work, the uncoordinated (vector) method of mathematical operations on vector values is used, for example, to prove the theorems of point and solids kinematics. This way in the educational process can reduce the time to prove some theorems on the course "Theoretical mechanics". Thus, in the study of kinematics of a point and solids, the vector functions of a scalar argument (time) are used: radius vector, velocity, acceleration, over which there is a need to perform a number of mathematical operations: finding their sum, vector and scalar product, and the product of vector functions on scalar, differentiation and integration, etc. As you know, there are two methods for conducting mathematical operations over vector values: a coordinate (or vector) that operates directly with vectors and coordinates - operations are performed over scalar quantities that are analytically determined in some coordinate system. The non-coordinate method is more compact and expedient for use in conducting theoretical studies. Using some properties of vector functions: the possibility of depicting a vector function of a scalar argument in the form of a product of a unit vector function (orth function) on a scalar function (a module of a vector function) and the rules of differentiation of vector functions, using the uncoordinated method, the proof of several theorems for determining the kinematic parameters of free points a solid body and a single point with its complex motion. The application of such methods of proving the theorems in the study of the discipline "Theoretical Mechanics" allows some time to be reduced to prove these theorems, which is an important factor in modern conditions.

#### Keywords

non-coordinate method; kinematics of solid body; vector function; scalar; derivative; radius vector; velocity; acceleration

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