4 comments on “Programming Clinic Four

  1. Damilare Agosu says:

    tr ⊗ ≡ 1 ⊗
    =( ⊗ 1 , 2, 3 + 1, ⊗ 2 , 3 + 1, 2, ⊗ 3) / (1, 2, 3)

    I dont really understand how to get to the next step from the one above

    =1/1(1, 2, 3 + 1, 2, 3 + 1, 3, 3)
    = 1 ⋅ 23 + 31 ⋅ 2 + 12
    ⋅ 3
    = 1 ⋅ 2311 + 3122 ⋅ 2 + 1233 ⋅ 3 =
    = ⋅ v

    • Damilare Agosu says:

      I didnt know it wasnt going to show the vectors and scalars.
      in slide7 page 26 the solution you solved i dont understand how the denominator of the trace was removed

      • oafak says:

        The denominator you are talking about is \left[ \bold{e}_1,\bold{e}_2,\bold{e}_3\right]. That is the triple product of the three orthonormal base vectors. It is not a good sign that it is not already obvious to you that it is the volume of a cube with all sides equal to unity! On that basis alone, we can conclude that, \left[ \bold{e}_1,\bold{e}_2,\bold{e}_3\right]=1. Another way to look at it is to remember that,

        (1)    \begin{align*} \left[ \bold{e}_1,\bold{e}_2,\bold{e}_3\right]&=(\bold{e}_1\times\bold{e}_2)\cdot\bold{e}_3\\ &=\bold{e}_3\cdot\bold{e}_3\\ &=1 \end{align*}

        Furthermore, in Q&A 1.35 it was shown that,

        (2)    \begin{align*} \bold{e}_i\cdot\bold{e}_j\times\bold{e}_k=\bold{e}_i\times\bold{e}_j\cdot\bold{e}_k=e_{ijk} \end{align*}

        Note that,

        (3)    \begin{align*} \left[ \bold{e}_1,\bold{e}_2,\bold{e}_3\right]&=(\bold{e}_1\times\bold{e}_2)\cdot\bold{e}_3\\ &=\bold{e}_1\cdot\bold{e}_2\times\bold{e}_3\\ &=e_{123}\\ &=1 \end{align*}

        These four ways of seeing the result should be obvious to you from Week Two lectures. You need to go back and work through that in order to have a fighting chance in the exams.

    • oafak says:

      You are NOT communicating! I do not know what you have in mind! Here are your choices:
      1. Learn Latex and write your questions to me in Latex.
      2. Write your questions by hand, denoting vectors with a bar, tensors with a double bar. Take a scan of the question on a Google drive and send a link to the scanned file.
      If you are making a reference to a specific item treated in the book, slides, tutorials or programming clinics, use this reference strategy: Chapter 3, Page 34 equation 5 is self explanatory; S8.15 will mean the week 8 slides, page 15; Tutorial 3.46 is tutorial 3 page 46; PC3.5 is the programming clinic slide 3, page 5.
      If you do not do any of these, you will need a witch to automatically know what is in your mind! I am not a witch!

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