JSXGraph solutions in theoretical mechanics courses for on-line education

Evgeny Bord

630008, Russia Novosibirsk 113 Leningradskaya Street

Abstract

Recent one and half year actualize problem on support education process out from campus with absence of blackboard and tools for control on students activity. This challenge seems more complex by circumstens by mobile communications usual for students community. Lose of traditional auditorial dialogue pose the problem of students motivation for education efforts in individual practice for solving academician tasks. On other hand this problem were exist for a lot of time and not issued from the choice between auditorial or distant form of education process. In russian enginereing education this problem seems to be common for courses on mathematics, physics, chemistry, theoretical, applied, enginering mechanics and other courses with essential containing of formal mathematical way of solution.

In this circumstance the JSXGraph package occures to be great, full admitabel and extremely usefull by this talk author point of view. Much more better one time see, than thousand times listen for comparison between dispaying of tangential line on function graphics and epsilon-delta definition of function derivative.

Figure 1: Browser workspace area in studying process.

On figure 1 presents some workspace of the browser in application developed with JSXGraph to regular students task in theme of material point kinematic. JSXGraph used for construction of material point trajectory, visualization of velocity and acceleration, tangential and normal components of acceleration. Visualization suggests to compare by students their solutions with right answer. This option serve two aims. First one is self-control of the solution by student, and another one is reducing of formal difficultes in finding the equation of trajectory. In application were using formal differentiation of arrow functions, object ‘conic’ from JSX library, MathJax processing for \LaTeX , notation in ’text’ objects construction.

Figure 2: Representation of hard copy printing materials in JSXGraph.

Technological background based on application of SVG format for internal representation of graphics images used in JSXGraph also essentially reduce problems with reaccomplish graphical materials prepared earlier for publishing in hard copy. On figure 2 represents an instance of those transfer.

System of objects in theoretical mechanics must include geometrical and analytical description with essential restriction by rigid body hypotises and inertial attributes for points and bodys. Common place in theoretical mechanics tasks is mix consideration by objects as alone free body, as connection and as part of outer system. This duality is one of essential difficulty for students in theoretical mechanics studying. JSXGraph in actual provide all necessary tools for modeling mechanical process in plane geometry, and accompanying study process. Lightweight package for interpretation operations on set, generation of function for interaction mechanical objects and visualisation of mutual properties of bodys and connections seems to be potentially conveniet addition to JSXGraph for theoretical mechanics.