A method for determining temperature stresses in a welded joint of a thin-walled pipe with a base is described. The method is based on experimental data of temperature measurement at reference points of the structure. The features of the elements of the welded joint made of carbon and high-alloy structural steels and the modes of electric arc welding were taken into account. The efficiency of using spline approximation of experimental data to obtain analytical dependences of the distribution of temperature fields and stresses, as well as to obtain a solution of the heat equation by numerical differentiation and integration for this case, is shown. Formulas for calculating temperature stresses for the case of an asymmetric temperature distribution in a cylinder under the action of a moving high-intensity heat source are obtained.

The features of modeling the dynamics of mechanical systems on the example of the operation of the tape drive mechanism related to real technological processes are stated. An approach to solving stiff systems of differential equations by the numerical-analytical method is noted. The approach is based on solving systems of higher-order differential equations using elementary functions using procedures for precision search for the roots of the characteristic polynomial of the system. A mathematical model of the tape drive mechanism of a VCR is given as an example of a precision electromechanical object.