Contents
Menu
Initial Conditions
Simulation Control
Properties of Virtual Camera
How to extract numerical data from the applet?
Localizing the Applet Into a Different Language
This program simulates rotation of a symmetric rigid body which is floating freely in weightlessness or which is fixed in its center of mass so that its motion is not affected by any torque. In Rigid Body menu it is possible to choose one of the following bodies: Plate, Disc, Elementary Plate, Sphere and Cuboid. These bodies differ in their principal moments of inertia.
The reference frame which you are going to observe from can be chosen in Reference Frame menu. You have two possibilities: Laboratory Frame which is fixed to inertial frame and Body-fixed Frame which is fixed to the rigid body.
Show menu allows you to select what should be visible during the simulation. The applet can display body, body-fixed axes, laboratory axes, vectors of angular velocity and of angular momentum and traces of end-points of visible vectors.
A mode of projection can be chosen in Projection menu. There are available two 3D views (with or without the perspective) and three projections to the main planes there.
Help menu allows you to display two documents. One of them
(Help...) is the document you are just reading and the second one
(About...) gives you some information on authors and license
conditions.
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Before starting the simulation one should tell the computer what the initial position of the body should be and how it should rotate at that moment. It
means that initial conditions give information about the state of the body at the beginning of the simulation. These initial conditions can be given by the
three Euler angles
,
and
,
that describe the initial position, and by their rates of change.
All these conditions can be set by six sliders placed at the bottom of the applet. Please, don't be afraid of Euler angles! After reading the text below (or after playing with the applet for a while) you will understand their meaning.
Euler angles are used for describing the orientation of a body in space. By rotating the body around the three main axes the body can be oriented in an arbitrary direction.
Consider laboratory frame S and its x, y and z axes and body-fixed frame S' with x1, x2 and x3 axes.
Let's start from the state where all Euler angles are zero. It means
S and S' frames are
identical. First rotate the S'
frame about the x1 axis counterclockwise by an angle
(fig. 1), then rotate it counterclockwise by an angle
about the z axis (fig. 2) and finally rotate it counterclockwise by
an angle
about the x3 axis (fig.3). Doing these three steps
you can orient the body in an arbitrary direction. And reversely: Having the body
oriented in any direction you can always find three Euler angles
which corespond to this state.
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Fig. 1. Rotation by an angle
|
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Fig. 2. Rotation by an angle
|
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Fig. 3. Rotation by an angle
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At this stage we are really ready to start the animation. Press the start button
.
The simulation will start and the function of this button will turn
into pause (its icon will look like this:
).
Pressing it again, its function will turn back into start and the
simulation will be interrupted. After yet another press the
simulation will go on starting at the stage when it was interrupted.
In order to stop it definitively press the Reset button. Step
back
and step forward
buttons do not need any explanation. The current simulation time (in
seconds) is displayed at the top left-hand corner.
After the initialization of the applet the body is displayed in 3D projection with perspective as it would be seen through a virtual camera. Pressing and dragging the left mouse button simultaneously you can change the view point of the camera. That is nothing else than turning all that virtual space another direction (whereas the Euler angles remain unchanged -- you are just changing your viewpoint!). Doing this while holding SHIFT key down you will change the zoom of your virtual camera (and of course the field of view will change, too) and while holding the CTRL key down you can move the field of view.
Position measurment: Choose floor, side, or frontal projection in the Projection menu. If you then drag your mouse above the display area of the applet, you will see coresponding coordinates of a point your mouse is just above. Position is given in decimeters.
Time measurement: Time is given in seconds and is displayed just above the Start button in the bottom part of the applet.
The applet uses also the following units: Mass is measured in kilograms. All the rigid bodies in the applet, except for an elementary plate, are homogenous and made from the same material with the density of 2.4 kg/dm3 (porcelain). The elementary plate is made of material particles, so its density cannot be defined. But the masses of its material particles are so chosen, that the elementary plate has the same principal moments of inertia as the disc.
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During the development of this applet we wanted to make it in such a way that all texts and labels might be easily translated into any different language without need for recompiling it. In order to translate it you just have to modify the source code of the html page which contains the applet.
The html applet tag has the following structure:
<applet code="name of main class" ...> <param name="name of parameter" value="value of parameter"> </applet>
Changing these parameters you can affect initialization of the applet. The first parameter is language. If its value is set to en, all the other parameters will be ignored and English texts will be displayed in the applet (these texts are stored in applet and they cannot be changed). If value of this parameter is set to anything else, e.g. sk, texts in the following parameters will be used and displayed in applet instead of default English texts.
For example the parameter which holds information about text on Reset button may look like that:
<param name="paramReset" value="Reset">
It means only that value of paramReset parameter contains string “Reset” and this string will be displayed on the Reset button.
In case it is needed to translate the help documents (text you are reading just now) you have to extract the FeynmanPlate.jar archive file. In fact it is only ZIP archive so you can rewrite the extension into .zip and extract it. Help documents are html pages help.html and about.html and they are located in feynmanplate folder in archive. Having translated it just create a new .jar archive with correct help documents.