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Mathematic Methods HW Solutions 49

# Mathematic Methods HW Solutions 49 - Chapter 10 4.4 4.5 4.6...

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Chapter 10 4.4 I = 2 15 π - 1 0 - 1 π 0 0 0 π Principal moments: 2 15 ( π - 1 ,π,π + 1); principal axes along the vectors: (1 , 1 , 0) , (0 , 0 , 1) , (1 , - 1 , 0). 4.5 I = 4 0 0 0 4 - 2 0 - 2 4 Principal moments: (2 , 4 , 6); principal axes along the vectors: (0 , 1 , 1) , (1 , 0 , 0) , (0 , 1 , - 1). 4.6 I = 9 0 - 3 0 6 0 - 3 0 9 Principal moments: (6 , 6 , 12); principal axes along the vectors: (1 , 0 , - 1) and any two orthogonal vectors in the plane z = x , say (0 , 1 , 0) and (1 , 0 , 1). 4.7 I = 1 120 4 - 1 - 1 - 1 4 - 1 - 1 - 1 4 Principal moments: parenleftbigg 1 60 , 1 24 , 1 24 parenrightbigg ; principal axes along the vectors: (1 , 1 , 1) and any two orthogonal vectors in the plane x + y + z = 0, say (1 , - 1 , 0) and (1 , 1 , - 2). 5.5 1 if jk = mn (6 cases); - 1 if jk = nm (6 cases); 0 otherwise 5.6 (a) 3 (b) 0 (c) 2 (d) - 2 (e) - 1 (f) - 1 5.7 (a) δ kq δ ip - δ kp δ iq (b) δ ap δ bq - δ aq δ bp 6.9 to 6.14 r , v , F , E are vectors; ω , τ , L , B are pseudovectors; T is a scalar. 6.15 (a) vector (b) pseudovector (c) vector 6.16 vector (if V is a vector); pseudovector (if
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