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Homework Help: Help with index notation

  1. Oct 9, 2004 #1
    hello, i just started learning index notation in my engineering class, and im having some trouble. one of the problems on my hw was:

    putting this in index notation:
    [tex]\vec{f}=g \frac{m_1m_2}{\vec{r}^2} \ \frac{\vec{r}}{\sqrt{\vec{r}^2}}[/tex]

    and then another problem that reads...

    consider a plane with outer normal vector [tex] v_i [/tex] on which a force is acting [tex] f_i [/tex]. what are the normal components of force on the surface? wut is the max shear component? what direction is the max shear component pointing? write this in index notation.

    i can figure out the components...just not how to write them in index notation. so any help here would be appreciated. thanks
     
    Last edited: Oct 10, 2004
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  3. Oct 9, 2004 #2

    arildno

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    For your f, you may write:
    [tex]f_{i}=\frac{Gm_{1}m_{2}}{r_{j}^{2}}\frac{r_{i}}{\sqrt{r_{k}^{2}}}[/tex]
    I read "g" as "G" ; hope I was right about that..:wink:
     
  4. Oct 9, 2004 #3

    robphy

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    [tex]f^a=g \frac{m_1m_2}{(r_b r^b)^{3/2}} \ r^a[/tex]


    Given a vector [itex]\vec f[/itex] and a unit-vector [itex]\hat n[/itex],
    the vector component of [itex]\vec f [/itex] along [itex]\hat n[/itex] is
    [itex](\vec f\cdot \hat n)\hat n[/itex].
    In index notation,
    [itex]( f^a g_{ab} n^b) n^c[/itex], where [itex]g_{ab}[/itex] is the Euclidean metric tensor and [itex]n^a g_{ab} n^b=1[/itex].
     
  5. Oct 10, 2004 #4
    for the problem with the normal vector and external force, arent the components fsin and fcos? how would i turn those into index notation?
     
  6. Oct 10, 2004 #5

    robphy

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    [tex]f^a g_{ab} n^b=\vec f\cdot\hat n =|\vec f | |\hat n|\cos\theta _\text{between f and n }=|\vec f | \cos\theta _\text{between f and n }[/tex]
     
  7. Oct 10, 2004 #6
    hmmmm [tex]g_a_b[/tex] ......that sounds like the matrix [tex]B_i_j[/tex] my prof was talking about. im unfamiliar with the term Euclidian metric tensor...but am i right in calling it a matrix?
     
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