GRAPHIC COMPUTER TECHNOLOGIES FOR DESIGN OF NON-CHAOTIC MECHANICAL SYSTEMS

Abstract

The application of technology for designing mechanical systems, which are based on elements of computer graphics, is considered. The work develops the themes of works where graphic computer technologies were used to study pendulum mechanical systems. Those. calculating the parameters of a mechanical system so that its pendulum oscillations become periodic (non-chaotic). For the development of research, it is necessary to apply computer graphic design technologies to other mechanical systems in order to provide their movements with technological not chaotic due to the selection of acceptable parameter values. The work uses the Lagrange method for conservative dynamical systems. To determine the approximate solution of the system of Lagrange equations of the second kind, it is necessary to coordinate the allowable values ​​of the system parameters with each other using the projection focusing method. These stages are carried out by graphical constructions in the environment of the maple package. Problems are solved as examples of the application of graphic technologies.

1. To develop options for ensuring the horizontal movement of the trolley due to non-chaotic oscillations of the pendulums associated with this trolley. Namely: a) two pendulums (on opposite sides of the cart); b) two pendulums under the cart; c) one spring pendulum under the cart.

2. Develop a method for calculating vehicle vibrations using the following example: a) railway car vibrations; b) oscillation of a trailer for the transport of dangerous goods.

3. Develop a method for determining the trajectory of the payload of a trebuchet machine for options: a) as a catapult for launching unmanned vehicles; b) as trebuchet with vertical movement of the counterweight.

Keywords: computer graphics, Lagrange equation of the second kind, projection focusing method, trebuchet machine.