"If a map, φ, carries every point on manifold M to manifold N
Figure 4.4: Illustration of a tangent ﬁber and the tangent bundle of a manifold.
Since acceleration is the time derivative of velocity, the material acceleration can be derived from the definition of material derivative as follows:
Using only direction of vector
UNIT 2: DERIVATIVES
For an alternative derivation, we can make use of the usual vector operations to express the total second derivative of the absolute position vector r.
Vector addition for vectors at any angle | Adding vectors | How to add vectors
Vector addition for perpendicular vectors | Adding vectors | How to add vectors