IMPLEMENTATION IN SСAS KIDYM OF SOFTWARE DETERMINATION OF DIMENSIONS OF UNKNOWNS IN PROBLEMS OF MECHANICS BASED ON ENERGY RELATIONS

Abstract

The paper presents the results of the study of an algorithm for processing measurement units of physical and geometric quantities in the problems of mechanics implemented in the specialized computer algebra system (SCAS) KiDyM. The KiDyM software complex is used for solving problems of mechanics of engineering and scientific orientation of any complexity. For the completeness of the initial data preparation process for such tasks, the use of measurement units in the initial and resulting data is essential. The output data of KiDyM tasks have a rather slow appearance due to their ana- lytical form. To provide assistance to the user, KiDyM programs have a special diagnostic block of output data. Therefore, the implementation of the dimensions used in KiDyM data pursues the additional goal of increasing the diagnostic capabilities of the system. Dimensional formulas are imple- mented here as ordinary analytical expressions, which enables the built-in computer algebra system to form expressions of data measurement units during their computer analytical transformations in the process of solving problems of dynamics, statics and kinematics. Thus, working out the meas- urement units in the SCAS KiDyM includes reading the values of the variables with the dimensions specified in formula form the initial data, diagnos- ing the correctness of dimensionising and compliance of the dimensions with the data, storing them in instances of the "variable" and "element" classes, calculating the dimensions according to data conversion formulas to obtain calculation results. The paper demonstrates how to efficiently es- tablish dimensions of geometrical and physical quantities using energy relations between coordinates and characteristics of elements of the mechanical model. For the demonstration of the logic of the implemented algorithm, simple compact examples from educational problems of kinematics, statics, and dynamics of flat and spatial systems are provided. The article shows how KiDyM constructs the necessary equations for solving tasks, and how units of measurement for equation components and their solutions can be obtained. Since dimensions are represented as formulas here, their simplifica- tion – reduction and substitution with derivative units – can be easily implemented. Moreover, since the variables involved in dimension formulas and the variables of the task itself, within KiDyM, are situated in different data spaces, they can have the same names without any confusion.