In Cartesian coordinates in velocity space (refer to Fig. 1), with the components expressed in spherical coordinates ( v, θ, ϕ), we have

(a) Show that the dyad (vv)/v² can be written in matrix form as

(b) Prove the following orthogonality relations

with i, j, k = x, y, z and where δ_ij is the Kronecker delta.

Figure 1.

Transcribed Image Text:

v = vv = v(sin cos ov+sin sin vy + cos 0 v₂)