Tangential and Normal Components of Acceleration Vectors

Given a parametrized curve , the velocity and acceleration are often expressed as a combination of two orthogonal unit vectors for each time .

We have

  • as the unit tangent vector which is tangent to at time ,
  • and as the unit normal vector to which is orthogonal at time , By definition, the dot product .

More precisely,

  • is defined as
  • is defined as

Fact:

Where is the derivative of the speed, and is a constant coefficient that we called curvature (which measures how much a curve “bends”)

Binormal Vector

In 3d, the binormal vector is defined as the cross product of tangent and normal vector

Reference


tags:vector curvedefinitions