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AN EXAMPLE OF USING COMPUTER ALGEBRA MAXIMA IN THE DISCIPLINE “COMPUTER MODELLING” // Tomsk State Pedagogical University Bulletin. 2015. Issue 12 (165). P. 86-92

The article deals with the modelling of pilot falling from a height of 6 000 meters in water. It is shown that the use of computer algebra system (CAS) Maxima qualitatively improves the consideration of the topic “Freefall considering environmental resistance”, traditionally studied in the discipline “Computer simulation”. Maxima has found the general solution of the nonlinear differential equation and found a partial solution with zero initial conditions – the Cauchy problem. CAS Maxima has found the analytical expression for the rate of fall and height fallen down as the functions of time. CAS Maxima has obtained the asymptotic behavior of the rate of fall in the time and has calculated the rate limit of fall. CAS Maxima calculated numerically intermediate values of fall speed and height fallen down for the 15 time values in the range of 1–15 in increments of 1. These values are compared with analogical values calculated by numerical method in book, with the standard deviation for rate is equal 2 %. CAS Maxima has plot graphics the rate of fall versus the time.

Keywords: model, computer modeling, computer algebra Maxima, integrated programming language, cycle operator, differential equation, initial conditions, Cauchy problem, free-fall, force of gravity, force of resistance, Archimedes force, Stokes’ law, drag coefficien