DIDACTIC POSSIBILITIES OF COMPUTER MODELING OF BODY MOVEMENT ON LESSONS AT PEDAGOGICAL UNIVERSITY

The didactic possibilities of the body movement modeling by replacing it with the material points system, which connected among themselves by weightless viscous elastic rods, are discussed. It is shown that the modeling of the body by a system of particles bound by viscoelastic weightless rods, obeying the basic law of dynamics, really allows: 1) to obtain the computer animation, i.e. the visual image of moving body at successive moments of time; 2) to plot the change of coordinates, velocities and accelerations of any of its points over time; 3) to model the translational, rotational, flat and spherical motion of the body, the interaction of the body with the surface or other body, to study the swimming of bodies, precession of the gyroscope and other phenomena; 4) to activate the mental activity of students, increase their motivation to learn. The tasks are considered: about collision of viscoelastic body with solid surface; about destruction of beam with defect; about the rotating wheel falling on surface; about flight of the rubber ring; about collision of two bodies; about the swimming of body with attached load; about the flexible ruler falling on cylinder; about the chain falling on cylinder; about the disk rotating on the horizontal surface; about the tumbling disk; about the gyroscope precession. The paper contains 8 figures obtained as a result of computer modeling of the above phenomena. As result of the analysis of the solved problems, it is shown that the modeling of a viscoelastic body by the method of bound particles has great didactic possibilities. It allows: 1) to study translational, rotational motion, deformation of bodies, gyroscope precession, etc., to update the knowledge of the relevant concepts and laws of mechanics; 2) to intensify the educational and cognitive activity of students, to increase their motivation for learning and its effectiveness; 3) to master the method of computer modeling, get acquainted with the solution of various professional tasks, explain the algorithms used and the simulation results at the school or pedagogical university level; 4) to develop the physical and algorithmic thinking, the ability to use the coordinate method and to perform information processing; 5) to organize an interactive dialogue between the student and the computer program; 6) to visualize information about the state of the object, build the trajectory of its points, the dependency graphs of coordinates and speeds on time; 7) to create various animations of body movement, to form a visual image of the corresponding phenomena; 8) to create problematic situations that require editing a computer program, changing system parameters, initial conditions and external influences; 9) to deepen the inter-subject connections between mathematics, physics and computer science.

Steering Control Method for an Underactuated Unicycle Robot Based on Dynamic Model

This paper proposes a lateral balancing structure based on precession effect of double-gyroscopes and its associated control strategy of the steering for an underactuated unicycle robot. Double-gyroscopes are symmetrically designed on the top of the unicycle robot and utilized to adjust the lateral balance of system. Such design can inhibit the disturbance of the gyroscope system to the pitch angle and is beneficial to maintain the lateral balance in the case of large roll angle fluctuations. Based on the analysis of the dynamics model, the gyroscope precession effects will be caused by the angular velocity of the bottom wheel and the roll angular velocity, i.e., resulting in a torque in the direction of the yaw. Then, a rapid response control strategy is proposed to use the torque to control the steering. Simulation results demonstrate the rationality of the lateral balance structure and the feasibility of the steering control method.