Question in linear algebra, derivation of a certain relation

In summary, the conversation is about trying to derive equation 9.30 and the confusion surrounding equation 9.32. The speaker explains how they interpret equation 9.32 and their approach to solving it, but they still do not arrive at the desired equation 9.30. They ask for help in identifying their mistake. A link to an image that may provide a better understanding of the equations is also provided.
  • #1
antonni
14
0
Hello good people,
please refer to this:
Pic.png


(notice the mistake in 9.31: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding)

Now, I am trying to derive 9.30 and for this, according to the book, we solve 9.32. The problem is I can not understand 9.32, the meaning of it.

I see it like this:

1) Group the strain tensor elements in each direction:
ST1=(s11+s21+s31)*e1 ; ST2=(s22+s12+s32)*e2 ; ST3=(s33+s13+s23)*e3
then the "s " stands for epsilon (strain) and the numbers are the strain element of the tensor.
e1,2,3 are unit vectors in S1,2,3 directions respectively.
2) Now, simply project the ST1,2,3 on the unit vector in the phi-psi direction, the h of 9.31. That way you get the magnitude of the strain in the phi-psi direction, which is what we want and what should be 9.30 according to the book. (of course s21=s12, s13=s31 & s23=s32)

I do it the like this:
component of ST1 on h = (h dot ST1) / |h| ; similarly for ST2 and ST3.
component of ST1 on h = (h dot ST1) / |h| = h1*(s11+s21+s31) ; similarly for ST2 and ST3.
As you can see I do not get the 9.30.

Where is my mistake?

Thank you very much

Anton
 

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  • #2
Hi there,

no one?
 
  • #3
hohohoo
 

Related to Question in linear algebra, derivation of a certain relation

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It is a fundamental tool in many fields such as physics, engineering, and computer science.

2. What is a relation in linear algebra?

In linear algebra, a relation is a connection or association between two or more sets of data. It can be represented mathematically as a set of ordered pairs or as a matrix.

3. How is a relation derived in linear algebra?

A relation in linear algebra is typically derived by observing patterns and relationships between data sets, and then using mathematical operations such as addition, subtraction, multiplication, and division to create a set of equations that represent the relationship.

4. What is the importance of deriving a relation in linear algebra?

Deriving a relation in linear algebra allows us to understand and analyze complex data sets and make predictions based on the relationships between them. It is also essential in solving real-world problems and developing efficient algorithms in various fields of science and engineering.

5. What are some common types of relations in linear algebra?

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