SECOND ORDER ODE

In this applet the equation, and the end values of variables on the diagrams, can be entered when "Function Input" is highlighted.

You can express the second derivative (d^{2}u/dt^{2})
as an arbitrary function of the variables u, du/dt (here called v),
and t.

Click "plot curves" when the equations and limits have been chosen.

Such equations normally have two free parameters. In this applet you
can fix u(t_{1}) and v(t_{1}) by dragging the rear of
the arrow to horizontal position (t_{1}) and vertical position
u(t_{1}) and adjusting the front end of the arrow so that the
arrow has slope v. (The arrow length does not matter, which means
that choosing a large arrow gives you more control of that slope.) If
you want to impose conditions at two different t values you can fix
one variable at one value and adjust the other until the other
condition is satisfied.

The slider controls the number of slices in the approximation used to compute the solution with the parameters you have chosen.

When the v box is checked, both the curves of u vs t and v vs t are displayed.

If you click on "Phase plane", you to see a plot of v vs u, as well as the plots of u and v vs t, but cannot see the equation and variable limits you have chosen.

This tool uses JQWidgets extensively. Please verify their copyright.

Developed by Daniel Kleitman and Jean-Michel Claus.

- Function input
- Phase plane

We define: v = du/dt

Show v = du/dt