Features of the Circle Simulation

• Number of Iterations. The number of iterations represents the number of times the ball will bounce in the circle and the number of points that will be plotted in the phase space. Since a ball can bounce only an integer number of times, an error message will appear if a fraction number is entered. An error message will also be displayed if a negative number is entered. By default, the number of iterations is set to 10. The user can change this number by clicking on the textfield next to "Iteration:". Once the box is activated, the user may type in the desired number. It is not necessary to press RETURN after entering the value. The number will be read when the START button is pressed.
• Initial Point. The initial point is starting position of the trajectory. The center of the canvas is (0,0). Both the x and y axes go from -150 to 150. By default, the initial point is set to (0,0). Since the canvas is made up of a finite number of pixel points, an error message will appear if a nonineger number is entered. After the user clicks on the START button, the initial point is tested to make sure it is inside the circle. An error message will be returned if it is not.
• Initial Velocity. The initial velocity is the direction of the ball from the initial point. By default the initial velocity is set to (1,1). The user may change the x and y vectors by selecting the textfields next to "Vx:" and "Vy:" respectively.
• Using Mouse to Input Values The mouse can be used to input values. An initial point can be selected by clicking the mouse on the desired point-- the textfields will changed accordingly. If the user does not select a point in the circle nothing will happen. If the user wishes to input a velocity with the mouse, he/she must hold the button down on the mouse after selecting the initial point and then drag the mouse until the line points in the appropriate direction. Once again the textfields will change.
• Speed. The speed controls how fast the ball moves in the circle. It may be adjusted by using the arrows.
• START Button. When the user presses the START button the program will run. If Both is selected, the trajectory of the ball be drawn in the canvas and the points will be plotted in the phase diagram. If Phase is selected, points will only be plotted in the phase diagram.
• CONTINUE Button. The CONTINUE button can be used if the user wishes to coninue iterating a trajectory. The START button must be pressed before the CONTINUE button. If the ratio, the initial point, or the initial veloctiy have been changed after the START button was pressed, the START button must be clicked again.
• OPEN PHASE DIAGRAM Button. The phase diagram is openned by clicking on the OPEN PHASE WINDOW button. After the phase diagram has been openned OPEN PHASE WINDOW button will change to CLOSE PHASE WINDOW and the user may click on it again the close the phase diagram.
• The Phase Diagram. The phase diagram can be closed by pressing the CLOSE button on the phase diagram or the CLOSE PHASE WINDOW on the main panel. The horizontal axis of the phase diagram is the length and the verticle the angle. By default, the phase diagram will show the horizontal angle on the verticle axis. To change to the tangent angle, the user must click on the GO TO TANGENT button. This button will change to GO TO HORIZONTAL when the tangent angle is on the verticle axis. The user can change between the two by pressing that button. The CLEAR button will clear all the points the phase diagram--both the horizontal and verticle plots. The START button on the phase diagram will start the program. If the user wants to select a point in the phase diagram, he/she must click in the phase diagram and the textfields in the main panel will change accordingly. A dot will appear on the selected point. The user can then press one of the START buttons. In the horizontal plot, a trajectory is not possible with some initial points and the velocities. In this case, the dot will not appear and textfields in the main panel will remain unchanged.