|
|
The helix r(t)=< 2 cos(2t), 2 sin(2t), t >, 0 ≤ t ≤ 2π .
- Red: unit tangent vector, T(t)
- Green: unit normal vector, N(t)
- Blue: unit binormal vector, B(t)
(Repeating in an endless loop.)
|
|
|
The helix r(t)=< 2 cos(2t), 2 sin(2t), t >, 0 ≤ t ≤ 2π .
- Red: unit tangent vector, T(t)
- Green: unit normal vector, N(t)
- Blue: unit binormal vector, B(t)
- Yellow: Osculating Circle
(Repeating in an endless loop.)
|
|
|
The elliptical helix r(t)=< 4 cos(2t), 2 sin(2t), t >, 0 ≤ t ≤ 2π .
- Red: unit tangent vector, T(t)
- Green: unit normal vector, N(t)
- Blue: unit binormal vector, B(t)
- Yellow: Osculating Circle
(Repeating in an endless loop.)
|
|
|
The "tornado" r(t)=< 2t cos(10πt), 2t sin(10πt), t >, 0 ≤ t ≤ 1 .
- Yellow: Osculating Circle
(Repeating in an endless loop.)
|
|
|
The "spiral" r(t)=< e-t cos(t), e-t sin(t), e-t >, 0 ≤ t ≤ 2π .
- Yellow: Osculating Circle
Question: why does the motion slow down so much as the particle approaches the bottom? Will it ever reach the bottom?
(Repeating in an endless loop.)
|
|
|
The "twisted cubic" r(t)=< t, t2, t3 >, -1 ≤ t ≤ 1; .
- Red: unit tangent vector, T(t)
- Green: unit normal vector, N(t)
- Blue: unit binormal vector, B(t)
- Yellow: Osculating Circle
(Repeating in an endless loop.)
|