Abstract:

Classical mechanics covers, amongst other subjects, the study of several concepts about the analysis of rigid body movements. For the students some of these concepts are difficult to understand, for the limited ability of abstraction and the movement visualization.

In this paper, the development of virtual worlds based on VRML code in order to help the visualization of some concepts of the classical mechanics is presented. These virtual worlds are available in the web address http://www.ehu.es/albizuri/. The visualization of these worlds is possible by mean of Web navigators (Internet Explorer, Mozilla Firefox, Google Chrome) with the installation of the adequate plug-in (in this case, the examples have been validated using the cortona VRML plug-in of Parallel-Graphics)

The selection of the mobile reference system, where the derivate of the angular velocity of the rigid body is zero or known, is facilitated by means of the visualization of the angular velocity vector and its movement. It is a very usefulness tool to understand the concept of the spatial and material derivate (also known as Law of Boure). Furthermore, by means of the VRML capabilities it is possible to define relative reference systems associated to solids or mobile reference systems that can be activated by clicking on the entity, and then the world relative movement for that observer is visualized (combining of “viewpoint” and “touchsensor” sentences).

In turn, by using successive sentences of “Orientation Interpolator”, it is possible to define the solid orientations as function of Euler angles. Also, by using successive sentences of “PositionInterpolator”, it is possible to define the translation motion. The first capability is the direct application in the definition and visualization of the Euler angles and their comprehension.

One of the most interesting of all problems in dynamics is that of Gyroscopic motion. This motion study can be made easier using VRML worlds. Several examples of the inertial or Euler-Poinsot gyroscope motions have been generated. Moreover, Lagrange gyroscope motion has been studied. In the same way, it is possible to visualize the space cone and body cone associated to the gyroscopic motion. It is possible to represent significant vectors (angular velocities or kinetic moments).

The generation of motion in two dimensions is simplified, because the position of each rigid body is defined by means of one rotation and two linear translations. In the case of plane kinematics, the visualization of motions in two dimensions, relative motion and graphic representation of body centrode and space centrode curves are the most interesting topics. It is very useful to facilitate the theoretical way the problem is set out.

Finally, the visualization of general motions of mechanical systems is possible. These motions can be obtained by numerical resolution of the differential equations and then they can be introduced in the VRML file.

Keywords:

vrml, classical mechanics, gyroscopic motion, absolute derivative, relative derivative, space.