Description of the Bezier curve is presented. We explain in detail creation of the calculation algorithm together with the resulting program. It also includes drawing of the base functions of the Bernstein polynomials. Firstly, the procedure is applied to the theoretical example given by ten control points in a plane which approximate the Bezier curve. Secondly, the application in which we have given 138 points of trajectory of real vehicle. Points are located in space and we use them again for approximation of the smooth Bezier curve.

In this contribution we present the methodology of the solution of ordinary differential equation by the Runge -Kutta numerical method of fourth order. Analysed function is continuous and it has derivatives at every point. Records of the centre of the gravity velocities of agricultural technological vehicle are function values of the derivatives. Algorithm of numerical integration was implemented by the help of programming language C# in MS Visual Studio Pro 2010 developing environment. Trajectory of the centre of the gravity movement in three-dimensional space is the result of the listed algorithm.

On selected polygon of control points we create Bézier curve. This we differentiate using a direct derivation of the polygon and receive hodograph of a new Bézier curve. The process is repeated for the second derivation, and these results are compared with numerical derivation of the parametric specified curve.

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.

In this contribution we are dealing with determination the center of gravity of agricultural machine in experimental way. The mathematical algorithm was based on the basic principles of the static equilibrium equations of the mass. The algorithm was implemented to the environment of PTC® Mathcad Prime® 4. Processing of experimental data was realized with Microsoft™ Excel® format table importing to the Mathcad Prime® software. Dislocation of center of gravity we set up for universal systemic carrier Reform Metrac H6X with front end mounted adapter. Measurements was realized with respect to the Slovak technical standard STN 27 8154. To measuring the mass of machine we used the scales Evocar 2000R manufactured by Tecnoscale Oy. Measuring was cooperated with the authorized subject Sloveko Ltd. From each measuring was created the weight statement. Measured data was processed with published mathematical procedure implemented to software and solved the coordinates of center of gravity with error estimation. Obtained result was compared with the manufacturer specification.