This figure shows the osculating ("kissing") circle of the helix at t = 0. (There is no animation for this figure.)
This figure shows T(0), N(0), and B(0). Click on the figure to
see the movie of T(t), N(t) and B(t).
This figure shows the osculating ("kissing") circle of the helix at t = 0. (There is no animation
for this figure.)
The ellipse x2/4 + y2/9 = 1 is shown in these figures.
The usual parametrization of this ellipse is
r(t) = < 2 cos(t), 3 sin(t) >.
The figure
on the left shows T in red and N in blue.
The other two figures show two osculating circles of the ellipse.
The middle figure shows a "typical" osculating circle, and the one on the right shows the
osculating circle at a point of maximum curvature. Click on any of these figures for
an animation.
These DPGraph figures show helices and the normal plane and/or
the osculating plane.
The helices are described by
r(t) = < cos(t), sin(t), Dz t / (2 p) >.
The helix moves "up" Dz, and goes "around" once, when
t increases by 2p.
helix (Dz = 1)
and normal plane (The plane is perpendicular to T.)
helix (Dz = 1)
and osculating plane
(The plane contains the velocity and acceleration vectors. This plane is perpendicular to B.)
helix (Dz = 1)
and osculating plane and normal plane
helix (Dz = 2)
and osculating plane and normal plane
This figure shows a helix made with a thin stip of paper. The lines in the paper
are approximately in the direction of T and B.
