I couldn't understand the exact geometrical meaning of the osculating plane definition. Can any one help me with this? Thanks advance.
Osculating plane: Let $\gamma$ be a smooth curve and P and Q be two neighboring points on $\gamma$. The limiting position of the plane that contains the tangential line at P and passes through the point Q as Q $\to$ P is defined as the osculating plane at P.
In another definition, osculating plane is a plane spanned by the tangent and normal line. But, I couldn't understand how we can find normal line geometrical?
Best Answer
https://youtu.be/dJ6q3ZV_kjE https://youtu.be/nLJy0B6CNMs Please see these videos, it may help you. The language is not English, but I hope you can understand it by the 3D presentation. However in simple language we can tell that, an oscillating plane is the plane containing curve's principal normal and tangent.