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Sherical distribution as a tensor?

  1. Mar 12, 2012 #1

    I have a 3D spherical distribution of mass in polar co-ordinates. The directional cosines of any point in the distribution are l, m and n. From which a 3x3 symetrical matrix, T, is constructed (shown below) using the idea of moments of inertia about a vector, derivation not shown here.

    l = sin θ cos ψ
    m = sin θ sin ψ
    n = cos θ

    T = [ Ʃl^2 Ʃlm Ʃln
    Ʃlm Ʃm^2 Ʃmn
    Ʃln Ʃmn Ʃn^2 ]

    My question, is T a tensor? If so how would I proove this? Invariants?


    Last edited: Mar 12, 2012
  2. jcsd
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