Math 2.0

concept

Arc length parametrisation

Summary

An arc length parametrisation of a regular curve uses the distance travelled along the curve as the parameter. In this parametrisation the curve has speed 11 at each point.

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To read this node, read these 8 nodes in this order. The foundations come first, and the list ends with this node.

Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptVector-valued function, concept, no evidence levelVector-valued functionconceptParametrised curve, concept, no evidence levelParametrised curveconceptRectifiable curve, concept, no evidence levelRectifiable curveconceptTangent vector of a curve, concept, no evidence levelTangent vector of a c…conceptRegular curve, concept, no evidence levelRegular curveconceptArc length parametrisation, concept, no evidence levelArc length parametris…concept
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Vector-valued function concept
  4. Parametrised curve concept
  5. Rectifiable curve concept
  6. Tangent vector of a curve concept
  7. Regular curve concept
  8. Arc length parametrisation concept

Sources

  1. Web https://en.wikipedia.org/wiki/Differentiable_curve, Length and natural parametrization

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Definitions