Calculus Animations,Graphics and Lecture Notes

Unit Tangent Vectors/Unit Normal Vectors

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A particle can acclerate in 2 ways, either a change in direction or a change in speed.

The purpose of this discussion is to formulate velocity and acceleration of a particle at a point in terms of vectors tangent and perpendicular to the trajectory at this point.

It is broken into 4 parts:

1. A discussion of  the unit tangent and unit normal vectors

2. Arclength parameterization

3. Curvature

4. Formulating the acceleration in components aT and aN - the tangential anf normal components . 

Notes - Unit Tangents and Unit Normals

Animation 1

Animation 2

The following are the notes and animations for a 3D example of unit tangents and unit normals
for a helix.

Notes - Unit Tangent and Unit Normal for a Helix

Animation 1

Animation 2

Notes- Arclength Parameterrization

Animation 1

Animation 2

Notes- Curvature

Notes- Tangential and Normal Components of acceleration



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