Analytical Mech Homework Solutions 6

Analytical Mech Homework Solutions 6 - 1 Rotate thru about...

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1.15 1. Rotate thru φ about z-axis 45 = D R 2. Rotate thru θ about x’-axis 45 = D R 3. Rotate thru ψ about z’-axis 45 = D R 11 0 22 0 R   =− 00 1  10 0 0 0 R = 0 0 R 1 () 1 2 11 1 ,, 2 R R ψθ ψθφ −+ == −− + 2 2 1 RR or 1 0, , 0 R α β γ     =   Condition is: x Rx ′ = KK where x 1 0 0 K = and x = K Since 1 x x ⋅= we have: 222 1 ψβ + += After a lot of algebra: 12 , 24 , =+ 1 2 = 1.16 ˆˆ vv c t τ K ˆ vc av nc n b ρ K ± 2 ˆ t 6
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