Multivariable calculus 1.4 - Dyadic product and tensors of rank 2
Автор: Anders Goude
Загружено: 2024-03-08
Просмотров: 455
This video is an introduction to the third way of multiplying vectors, which is the dyadic product. It also serves as a small introductions to tensors of rank 2.
This video will use the matrix notation for tensors, but as it is an introduction, I will not covers concepts, such as co-variance and contra-variance, and here, all vectors are considered equal.
I will not go that deep into tensors of rank 2, but we will come in contact with them later when we calculate the gradient of vectors, and we do have them in fluid mechanics
0:00 Matrix notation and dot product
1:58 The dyadic product
3:57 Dot product between vector and dyadic product
6:07 Dot product between dyadic product and vector
8:27 Properties
9:12 Example - Inertia tensor
13:38 Derivation of inertia tensor
15:54 Example - Stress and strain (strain)
21:59 Example - Stress and strain (stress)
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