# Sherical distribution as a tensor?

1. Mar 12, 2012

### Dr Bwts

Hi,

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?

Thanks

Nic

Last edited: Mar 12, 2012