Abstract
The design an optimal numerical method for solving a system of ordinary differential equations simultaneously is described in this paper. System of differential equations was represented by a system of linear ordinary differential equations of Euler’s parameters called quaternions. The components of angular velocity were obtained by the experimental way. The angular velocity of the centre of gravity was determined from sensors of acceleration located in the plane of the centre of gravity of the machine. The used numerical method for solving was a fourth-order Runge-Kutta method. The stability of solving was based on the orthogonality of a direct cosine matrix. The numerical process was controlled on every step in numerical integration. The algorithm was designed in the C# programming language.
Highlights
The goal of this contribution is that the published research supplement the missing part of many scientific books and scientific articles dealing with spacecraft attitude dynamics of rigid body movement in three-dimensional space
We are dealing with design an algorithm for numerical solving a simultaneous system of differential equations (SSDE)
We chose the quaternion differential equation, where the angular velocities we got from the real experiment with an agricultural machine
Summary
The goal of this contribution is that the published research supplement the missing part of many scientific books and scientific articles dealing with spacecraft attitude dynamics of rigid body movement in three-dimensional space. Determination of the dislocation of a certain moving frame of the system is a very important part of applied dynamics. One of these cases refers to the robotic arms movement as defined in [5]. In even a specific case is the problem to determine the dislocation of the whole moving body in three-dimensional spaces. This case refers to a moving vehicle on the ground with respect to an inertial coordinate system. Using GPS giving only coordinates of moving objects with no acceptable precision. The data obtained from sensors of acceleration or gyroscopic gauge, giving the more
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