ATRACTOR

The applet is made up of what we call the viewing area (with a gray background) and menus with buttons, text boxes and value control bars (with a blue background). However, it is worth noting that, as we will see later, in some cases it is possible to also enter data directly into the display area.

Click the image where you have questions.

Note: The following figures are non-manipulable images. In the figures marked with , if you hover the mouse over them you will see an animation.

The display zone is divided into six areas:

• in the left area two pendulums are represented, formed by two balls of masses m and m, joined by a spring of resistance k and suspended by two rigid rods of length L and L.The balls are subject to the action of gravity, g. Use the mouse to drag the balls to the desired starting position;

• in the central area there is a representation of the potential, kinetic and total energies of the pendulums and also the energy of the spring (compressed or stretched), at each instant.

  Dragging the mouse in this area vertically allows you to zoom;

• in the right area (from top to bottom) are representations:
  • of the graphs of the functions x(t) and x(t), where x(t) and x(t) represent the measurements (in R) of the angles that the pendulums make with the vertical at time t;
  • the trajectory in the space of configurations which, in this case, is a torus;
  • of the vector of initial velocities of the two pendulums.

The initial parameters of the pendulums can be modified:

• in the case of the value of the initial angle that each pendulum makes with the vertical,
  • directly in the text boxes: and ;
  • dragging the pendulum ball;

• clicking on the yellow point on the torus, defining a new vector (as long as the cursor has the shape : more details).

 

• in the case of the initial velocity value,

• directly in the text boxes: and ;
• clicking in the lower right area, defining a new vector (as long as the cursor has the shape : more details).

• in the case of the values of the lengths (L and L), the masses (m and m) of the pendulums, the gravity (g) and the spring resistance (k):
  • entering the values in the text boxes;

  

  

  

   

  • dragging the control bars.

  

Once these values have been chosen, click , to see the simulation of the pendulum movement.

The menu has the following options:

• : to reset the time value (t = 0);
• : to return to the initial configuration.

Important note: to choose a point in one of the two areas at the bottom of the applet, always check that the mouse cursor has the following shape: . If it has another shape, like , click first. If it is and you want to change to simply right-click and in the window that appears choose the Rotate, Orbit option.

In the four areas on the right side of the applet, try clicking on them with the right mouse button: you get a menu with other options for manipulating objects.

Among the options, allows you to have a resizable window of the area where you clicked - for more information, click here.

The flag, at the top of the applet, indicates the language used. If you wish, click it and select another language:

By clicking , you can choose between:

• : access this instruction page;
• : accesses information about the applet version*.