The matrices of the equations of motion of the mechanical system formed in EULER are highly sparse and this is taken into account in the software implementation. Due to this, the calculation time is practically linear depending on the number of bodies of the system under study. Figures 1 and 2 show examples of two types of test problems: a chain of identical bodies connected by ball joints, and a rectangular lattice of identical bodies. The motion of systems occurs under the influence of gravity. The calculation time in both examples is well approximated by the power function k * nα, where n is the number of bodies in the system under study; k, α - coefficients, the values ​​of which depend on the type of the task, the characteristics of the computer and the settings of the calculation method in the software package. Test calculations show that not only the value of k depends on the characteristics of the computer and the settings of the calculation method, but also the value of α. For a chain of bodies α = 1.0 ÷ 1.15, for a grid of bodies α = 1.2 ÷ 1.4.

Figure 3 shows the time schedules for solving these tasks, depending on the number of bodies. The solution was carried out on a personal computer with an Intel Core CPU i7 950 @ 3.06 GHz. For numerical integration we used the fourth-order Runge-Kutta method with a constant step of 0.001 seconds. The duration of the process of motion of the systems is 1.0 sec. The position and velocity corrections were disabled.

Figure 1. The chain of bodies

Figure 2. The grid of bodies

Figure 3. Time for calculating test tasks

 

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