1.- Global Description.

The application \xe3 Particles" allows the simulation of the dynamics of particles which can interact through different forces and/or by external fields.

\xe3 Particles" is an application developed with the COLOS development tool XDEV. It was originally designed as a testbed for XDEV and also as an example for the use of that authoring system.

This application was originally developed in 2-dimensions and it is now also implemented in 3-dimensions. It takes many ideas from the \xe3 xyZET" application from Kiel.

2.- Scientific content - Important Features

The application allows the design of different experiments covering several concepts in mechanics and electricity, at an introductory level:

Kinematics (velocity and acceleration).
Dynamics (Hooks law, gravitation).
Energy concepts (potential and kinetic, conservation).
Coulomb interactions.
Magnetic force on moving charges.

Besides the already implemented interactions and external fields, the user, if XDEV expert, can access the source program. Here marks can be found where additional interactions or external fields can be easily added or modified. This converts the application into a more general environment where the teacher can design his/her own class to cover a specific topic of interest.

3. Didactical Approach.

The standard approach to cover the above mentioned topics can be found in any general physics text book, where the student can find everything related to the mathematical description of the forces and closed form solutions to different problems. Sometimes experimental work is available to show the behaviour of very simple systems.

With this application, an introduction to the basic concepts can be made, which hides much of the mathematical load usually involved when teaching those concepts. The graphical animation also allows a deeper understanding of those concepts, preparing the student for a much easier introduction to the mathematics behind the formal approach. The behaviour of complex systems, difficult to be dealt with in terms of an analytical approach, can also be shown.

4. Implementation

This program has been developed with XDEV with extensive use of the XcWorld or Xc3DWorld Widgets.

The application shows two different panels. The first presents the simulation, the second is used as control panel where the user interactively defines the kind of interactions or external fields acting on the particles. The velocities and accelerations for all the particles can be graphically displayed.

The particles are mouse sensitive for moving and changing of velocity. A strip-chart recorder has been implemented to show different quantities (energies, positions), allowing the students to link the visualization on the screen to standard graphical representations found in text books.

A numerical finite difference algorithm has been implemented to integrate Newton's second law: The force on a particle is first computed in terms of the present interactions and external fields. Then the new velocity is computed in terms of the acceleration and old velocity. Now the new position is computed in terms of the velocity and old position. This process is iteratively applied to all particles.

With a high powered workstation, the number of particles that can be involved in a simulation with no appreciable loss of speed is around 100. This is enough to get an idea of the behaviour of complex systems. For instance, the electrostatic behaviour of a conductor with fixed positive ions and free moving electrons can be easily shown.

No additional helps, besides a self-explanatory user interface design has been implemented.

5. Target Group

"Particles" is intended to be used for three different purposes:

As an environment for learning basic physics concepts at an introductory level, guided by a teacher or in a self-supporting way. For this last possibility, some additional support material should be provided by the teacher (parallel experiments, assignments, etc.).
As example for an application made with XDEV where a novice user of this authoring system can find many suggestions for solving his/her own design problems.
As a general environment where the XDEV-expert teacher can design his/her own classes, by modifying or adding interactions or external fields needed to show the particular phenomena under study.

6. Evaluation

Evaluation has been carried out only in the second modality mentioned above. This application was one of the first made with XDEV and has been taken as an example for different teachers to design their own software using XDEV.

It will be used during the present university course (introductory level), as support for teaching basic concepts in mechanics: velocity, acceleration, momentum and energy conservation. This will be done in combination with the Electronic Book application.

The Simulation Program PARTICLES

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