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TNB Frame with Osculating and Normal Planes

TNB Frame with Osculating and Normal Planes
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2018-09-28 00:45
VectorCalculusGeometric Construction
This example demonstrates the TNB frame with osculating and normal planes. It involves concepts from calculus such as derivatives and integrals. Using GeoGebra commands like CurveCartesian, NDerivative, and Vector, these geometric elements can be constructed. Suitable for calculus courses and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian((f(t), g(t), h(t)), t, -10, 10) → r
  2. NDerivative(r) → r'
  3. NDerivative(r') → r''
  4. Vector(r(b), r(b) + T) → u
  5. Vector(r(b), r(b) + N) → v
  6. Vector(r(b), r(b) + B) → w
  7. OrthogonalPlane(A, Vector[u ⊗ v]) → o
  8. OrthogonalPlane(A, Vector[v ⊗ w]) → n
  9. OrthogonalPlane(A, Vector[u ⊗ w]) → p

AI Drawing Prompt Reference

Draw a three-dimensional space curve, at a point on the curve show the tangent vector, normal vector and binormal vector (three mutually orthogonal unit vectors), through that point construct the osculating plane formed by tangent and normal vectors, the normal plane formed by normal and binormal vectors, and the rectifying plane formed by tangent and binormal vectors, displaying their spatial relationships.
The prompt above was compiled from the original drawing commands and is for reference only.