Vector Functions

Position

Velocity

Velocity is equal to the derivative of position with respects to time, ${\vec {v}}={\frac {d}{dt}}\,{\vec {r}}$

Tangent and Normal Vectors

The Tangent Vector is the unit vector tangent to the motion, ${\vec {T}}={\frac {\vec {v}}{\left\Vert {\vec {v}}\right\|}}$ . The Normal vector, similarly, is the unit vector normal to the motion, ${\vec {N}}={\frac {\frac {d{\vec {T}}}{dt}}{\left\Vert {\frac {d{\vec {T}}}{dt}}\right\|}}$

Acceleration

Acceleration is equal to the derivative of velocity with respects to time, ${\vec {a}}={\frac {d}{dt}}\,{\vec {v}}$

Tangential and Normal Acceleration Vectors

Curvature/Radius of Curvature

Osculating Circle

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