And for polar angles µ, ˜ θ and θ , we assume they do not have τ -dependence, like µ ( σ$_{1}$, σ$_{2}$ ). With this choice, we can readily write down several constants of motion. They are momenta conjugate to those coordinates with linear τ -dependence, and it is natural to call them E, J$_{ψ}$, J$_{˜}$ $_{ψ}$, J$_{˜}$ $_{φ}$, J$_{φ}$ . It is easy to infer that E gives conformal dimension, J$_{ψ}$ gives R- charge, and J$_{φ}$ gives the spin quantum number of SU (2) global symmetry, for the dual operators in the field theory. Maybe it is not immediately clear how the SU (3) angular momenta J$_{˜}$ ψ and J$_{˜}$ φ give the weight vector of a given state. Let us follow the the standard convention and define the Cartan subalgebra with Gell-mann matrices for the fundamental representation. Then it turns out that we can relate J$_{˜}$ φ with λ$_{3}$ , and J$_{˜}$ ψ − 2 J$_{ψ}$ with λ$_{8}$ . This adjustment will be justified when we study particle-like solutions. Below we record the expressions for various conserved quantities of spinning membrane configurations. We have introduced new symbols Δ ≡ E, R ≡ 8 J$_{ψ}$, Q$_{3}$ ≡ 2 J$_{˜}$ $_{φ}$, Q$_{8}$ ≡ 2 √ 3( J$_{˜}$ ψ − 2 J$_{ψ}$ ) , J$_{3}$ ≡ 2 J$_{φ}$ for later convenience, and √ λ ′ = L $^{2}$/ 2 λ $^{0}$. 8 λ$_{3}$ = 1 2     1 0 0 0 − 1 0 0 0 0$^{}$    , λ$_{8}$ = 1 2 √ 3     1 0 0 0 1 0 0 0 − 2$^{}$    , (24) Δ = √ λ $^{′}$κ , (25) R = √ λ ′ 8 ∫ dσ 2 (2 π ) 2 $^{[}$ζ + 3 sin 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) + 2 ω cos θ ] , (26) Q$_{3}$ = 3 √ λ ′ 32 ∫ dσ 2 (2 π ) 2 $^{{[}$ζ + 3 sin 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) + 2 ω cos θ $^{]}$(sin 2 µ cos ˜ θ ) +4 sin 2 µ $^{[}$sin 2 ˜ θν$_{2}$ + cos 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) cos ˜ θ ]} , (27) Q$_{8}$ = √ 3 λ ′ 32 ∫ dσ 2 (2 π ) 2 $^{{[}$ζ + 3 sin 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) + 2 ω cos θ $^{]}$(3 sin 2 µ − 2) +12 sin 2 µ cos 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) } , (28) J$_{3}$ = √ λ ′ 16 ∫ dσ 2 (2 π ) 2 $^{{[}$ζ + 3 sin 2 µ ( ν$_{1}$ + cos ˜ θν$_{2}$ ) + 2 ω cos θ $^{]}$cos θ +4 sin 2 θω } . (29)