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747_Dynamics 11ed Manual

# 747_Dynamics 11ed Manual - ⎟ ⎟ ⎠ x y z ⎛ ⎜ ⎜...

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Engineering Mechanics - Dynamics Chapter 21 The space capsule has mass m c and the radii of gyration are k x = k z and k y . If it is traveling with a velocity v G , compute its angular velocity just after it is struck by a meteoroid having mass m m and a velocity v m = ( v x i + v y j + v z k ). Assume that the meteoroid embeds itself into the capsule at point A and that the capsule initially has no angular velocity. Units Used: Mg 1000 kg = Given: m c 3.5 Mg = m m 0.60 kg = k x 0.8 m = v x 200 m s = k y 0.5 m = v y 400 m s = v G 600 m s = v z 200 m s = a 1m = b 1m = c 3m = Solution: Guesses ω x 1 rad s = y 1 rad s = z 1 rad s = Given a c b m m v x v y v G v z × m c k x 2 0 0 0 k y 2 0 0 0 k x 2
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Unformatted text preview: ⎟ ⎟ ⎠ x y z ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ = x y z ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ Find x y , z , ( ) = x y z ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ 0.107 − 0.000 0.107 − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ rad s = Problem 21-39 Derive the scalar form of the rotational equation of motion along the x axis when Ω ≠ ω and the moments and products of inertia of the body are not constant with respect to time. 745 Problem 21-38...
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