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 * n?, where n is the number of bodies in the system under study; k, ? - 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 ?. For a chain of bodies ? = 1.0 ? 1.15, for a grid of bodies ? = 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


Latest news

Euler version 12.12

A new version of the software package has been released
EULER 12.12 
The demo version 12.12.03 of the software package is available at the link

DOWNLOAD the demo version of EULER

May, 2023

Версия Euler 12.12

Выпущена новая версия программного комплекса
EULER 12.12

Май, 2023

Update of the EULER software package - version 12 has been released

We continue to actively work on improving the EULER software package.

A big update of the software package - the 12th version of EULER has been released, in which the following important changes have been made:

  • a new computational core with significantly expanded capabilities has been developed;
  • increased calculation speed;
  • implicit integration methods are implemented, the use of which reduces the calculation time of rigid systems by orders of magnitude;
  • a number of user interface improvements have been made.
Euler version 11.14

A new version of the EULER 11.14 software package has been released

December, 2020