Abstract:

The dynamics of a particle represents an important chapter of the discipline mechanics taught in engineering faculties. Despite its apparent simplicity, the subject involves numerous theoretical aspects that, under various forms, are applied to the dynamic study of most mechanical systems, such as: modeling the system, determining the mathematical expressions of the forces that act upon the system, deducing the differential equations of motion, integrating these equations, determining the integration constants and deducing the equations of motion of the system and determining the geometrical characteristics of the motion.

The teaching practice has shown that understanding the topics of the discipline is much facilitated by solving simple applications, such as the motion of a particle in a uniform gravitational field, without and with drag force, respectively. However, the traditional presentation method, with the chalk on the blackboard, involving several mathematical procedures, can seem laborious and annoying to students. The authors developed a computer code dedicated to the above-mentioned application, to serve as a teaching aid for the practical application sessions of the dynamics course. The basic requirements considered in code development were to preserve clarity and simplicity in problem definition and results display, while providing an intuitive illustration of the particle motion. Thus, the program uses a minimalistic interface, centered on the animated representation and designed to focus students’ attention to the particle trajectory peculiarities. Forces acting on the particle are also dynamically displayed. The trajectory is computed in real time, depending on the input parameters, such that the students can easily observe the influence of the initial values of the parameters on the motion and can use the output data in order to check the results of their own hand calculations.

The practical sessions that include the use of the program consist of the following successive steps:
a) brief reminder of the relevant topics taught at the course;
b) short explanation on the use of the program;
c) guided definition of the first set of parameters, including running the program and observing the results;
d) additional free exercises, if necessary, to allow students get used with program use;
e) variation of system parameters to obtain characteristic cases and comparison of obtained results (e.g. influence of drag force, influence of initial angle etc.);
f) discussion and comments.

The session is led by the instructor, which encourages students to interact and to experiment. The instructor is also supposed to keep an adequate pace of the session and to explain each set of results, with reference to course topics. The program integrates in a larger package, developed by the authors over the past one and a half decade as a virtual laboratory of dynamics.

Keywords:

Virtual laboratory, animated graphical representation, uniform gravitational field, drag force.