How to use
Enter functions f (t), g(t), and h(t) in the text input fields marked "f(t)=", "g(t)=", and "h(t)=".

 Example: f (t)=3cos t, g(t)=3sin t, h(t)=t/3

Click the "Graph" button (this button also refreshes the graph).

Rotate the graph by clicking and dragging the mouse on the graph.

Enter first derivative functions f '(t), g'(t), and h'(t) in the text input fields marked "f'(t)=", "g'(t)=", and "h'(t)=".

Click the "Graph" button.

 Example: f '(t)=-3sin t, g'(t)=3cos t, h'(t)=1/3

Enter second derivative functions f ''(t), g''(t), and h''(t) in the text input fields marked "f''(t)=", "g''(t)=", and "h''(t)=".

Click the "Graph" button.

 Example: f ''(t)=-3cos t, g''(t)=-3sin 3t, h''(t)=0

Click the "+" and "-" buttons under the field marked "t=" to change the position at which the vectors are drawn on the graph. (Holding a button down causes its action to be repeated.)

To erase the graph and all input fields, click the "Clear" button.


Examples
 Helix: f (t)=3cos t, g(t)=3sin t, h(t)=t/3, with appropriate derivatives

 Wavy circle: x=3cos(t), y=3sin(t), z=sin(2t), with appropriate derivatives


Other Notes
The parametric path itself is shown in blue. The velocity vector v(t)=<f '(t), g'(t), h'(t)> and acceleration vector a(t)=<f ''(t), g''(t), h''(t)> are shown in orange. The standard unit tangent vector T is defined to be the unit vector in the direction of the velocity vector v(t) The standard unit normal vector N is defined to be the unit vector for which the acceleration vector a(t) lies in the T-N plane, with component aN (the length of the projection of a(t) onto N) being positive. The standard unit binormal vector B is defined so that B=TxN. The unit vectors T, N, and B are shown in green. Labels show the values of aT (the tangent component of a(t)) and aN (the normal component of a(t)).