Φ=3y12+2y22-3y1y32
Find: div(gradΦ).
I broke it down to find the partial derivative of all 3 coordinates y1,y2 and y3, so using the continuity equation:
y1=6y1-3y32
y2=4y2
y3=6y3y1
However, I'm not sure if this correct, would the first part give the gradient? Could someone confirm or solve...
I am having trouble converting [D]=[A][ B]T[C] to index notation.
I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct.
Would anyone be able to elaborate on this?
Regards
1. Deriving frequency in a beam equation, E=Young's Modulus, I = Moment of Inertia, m=mass, L=length, f=frequency.
2. Deriving this equation: (∏/2)√(EI/mL3)
3.(EI(∂4y/∂x4 = -m(∂2y/∂x2) ≈ EI(∂4y/∂x4+ m(∂2y/∂x2 = 0
Don't know where to go from here...