Application of differential geometry in agricultural vehicle dynamics

Abstract

This paper deals with the application of differential geometry methods to a precise calculation of the length of trajectory of an agricultural mechanism that moves on a sloping terrain. We obtained technical exciting function from experimental measurements, out of which we obtained the function of Euler's parameters by using computer processing. The processing of these parameters provided translational and angular velocities of the gravity centre of the systemic vehicle MT8-222, which performed the determined mounted manoeuvres. We obtained differential equations that describe the function of a spatial curve by the application of differential geometry methods. The length of the curve is obtained by a numerical solution of the differential equations formed. We used Dormand-Prince numerical method for the numerical solution. Next, we evaluated the error of the numerical integration for every calculation by reason of the stability of computation. We also addressed the geometric characteristics of the curves such as the radius of curvature. The mounted manoeuvres as well as the corresponding velocities, trajectories, and radiuses of curvature were processed in a graphic way.

Keywords

• trajectory modelling
• numerical integration
• radius of curvature