237_Problem CHAPTER 9

237_Problem CHAPTER 9 - PROBLEM 9.164 CONTINUED Alternative...

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PROBLEM 9.164 CONTINUED Alternative solution for part a The equation of the included face of the tetrahedron is 1 xyz abc + += so that 1 x z yb ac  =−   For an infinitesimal element of sides , , dx dy and dz dm dV dydxdz ρ = = From part a 1 z xa c Now () ( ) ( ) 11 00 0 x zz ca c b zx I zxdm zx dydxdz −− == ∫∫ ( ) 1 1 z c x z zx b dxdz   ( ) 1 3 22 0 0 111 232 z c a c xz bz x x d z  23 2 2 0 1 2 c z z bz a a a d z c c c 3 2 0 1 1 6 c z ba z d z c 4 2 0 1 33 6 c z ab z d z c cc + 345 2 0 13 1 24 5 c mz
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