Example: Stability of Torque Free Motion From(3)→d2≈≡ constant Differentiate(1)and substitute value of iy from(2) (Iy -I2)(Iz 0 , n-An=0,A=(1-b2- Solutions, W= AeVAt +Be-VAr AERO Dynamics 16.07 Dynamics D25-D26 9Example: Stability of Torque Free Motion Dynamics 16.07 Dynamics D25-D26 9 From (3) → ωz ≈ ω ≡ constant Differentiate (1) and substitute value of ω˙ y from (2), → . . . Ixω¨x − (Iy − Iz)(Iz − Ix) Iy ω 2ωx = 0 or, ω¨x − Aωx = 0, A = − (Iz − Iy)(Iz − Ix) IxIy ω 2 Solutions, ωx = Ae √ At + Be− √ At