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- 2. Main goal of all external world discovery of investigations should be the rational order and harmony
- 3. Mathematical modeling is a specific form of the world cognition, which is able to translate the
- 4. Researcher studies objects of interest, watches the course of events, and interferes in them by asking
- 5. Simplified diagram of the cognition process Object of cognition Subject of cognition Model of the object
- 6. main stages of mathematical modeling
- 7. principles of the mathematical model construction It is possible to identify some common laws in the
- 8. After determination of the system functions and independent variables, we have to specify the coordinate system
- 9. Having written mathematical relations which express cause-and-effect relation for the phenomenon, we will find out that
- 10. Thus, the mathematical model usually includes three classes of characteristics. Parameters of the process in each
- 11. Process of construction mathematical model includes the following elements: Object of study Functions of the system
- 12. Now we have specific mathematical relations. They should be studied on the basis of various quantitative
- 13. classification of mathematical models Depending on the specifics of variables constituting mathematical models, we can specify
- 14. Stochastic models, which may have impact on the process random factors. Deterministic models, in which such
- 15. Equation of the falling body The first mathematical model, which meets all academic requirements is associated
- 16. If the velocity v of the body is known, we obtain the relation = v (l.l)
- 17. In the third stage of the study we will try to interpret the results. First of
- 18. Obviously, the position of the body will essentially depend on the exact position of the body
- 19. We again interpret the results and find out mismatch of calculated height of falling body to
- 20. The variation law of the body velocity is not known. Velocity of change of the function
- 21. Definition of the body height is reduced to finding its derivative (velocity). For calculation of velocity
- 22. Positive value g = -а is called free fall acceleration, and it is an absolute constant
- 23. Solving equation (1.8) with the initial condition (1.7), we find that the velocity of a falling
- 24. The additional information Then, based on the properties of the mathematical model we can get some
- 25. Another characteristic of the process, which has practical importance, is the body velocity at the falling
- 26. A final remark concerns the conditions of applicability of the mathematical model. The model describes the
- 27. Thus, the complete mathematical model of the process includes the state equations (1.1), (1.8) on the
- 28. main elements of the mathematical model of the falling body process
- 29. It should be noted that the results correspond to some particular level of study of the
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