MHB Vector Triple Product: Simplification Possible?

  • Thread starter Thread starter Dustinsfl
  • Start date Start date
  • Tags Tags
    Vector
Dustinsfl
Messages
2,217
Reaction score
5
Given the basis $\{\mathbf{b},\mathbf{c},\mathbf{b}\times\mathbf{c}\}$.
We define the triple vector product as
$$
\mathbf{b}\times(\mathbf{b}\times\mathbf{c}) = (\mathbf{b}\cdot\mathbf{c})\mathbf{b} - b^2\mathbf{c}
$$
Can this be simplified further? We don't know if b and c are orthogonal just that they are linearly independent.
 
Physics news on Phys.org
Re: basic vector question

I don't think you can simplify further.
 
Re: basic vector question

dwsmith said:
Given the basis $\{\mathbf{b},\mathbf{c},\mathbf{b}\times\mathbf{c}\}$.
We define the triple vector product as
$$
\mathbf{b}\times(\mathbf{b}\times\mathbf{c}) = (\mathbf{b}\cdot\mathbf{c})\mathbf{b} - b^2\mathbf{c}
$$
Can this be simplified further? We don't know if b and c are orthogonal just that they are linearly independent.

Nope.
Note that $\{\mathbf{b},\mathbf{b}\times\mathbf{c},\mathbf{b}\times(\mathbf{b}\times\mathbf{c})\}$ is an orthogonal basis.
Effectively you are looking at the Gram-Schmidt orthogonalization algorithm.
 
Thread 'Derivation of equations of stress tensor transformation'
Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
Back
Top