- #1

Dr Bwts

- 18

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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

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

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