(a) Explanation Given Information: The mass ( m ) of the satellite is 2500 kg. The height ( h ) of the satellite is 2.4 m. The base side ( B ) of the satellite is 1.2 m. The radii of gyration about x ( k x ) , y ( k y ) and z ( k z ) axis are 0.9 m, 0.98 m and 0.9 m respectively. The satellite is equipped with a main thrusters ( F ) is 500 N. The thrusters in A ( F A ) , B ( F B ) , C ( F C ) and D ( F D ) are 20 N. The thrusters ( Δ t ) A and B are activated for 2 sec. The satellite ( ω 0 ) is spinning at the rate of 36 rev/h . Calculation: Calculate the angular velocity ( ω 0 ) : ω 0 = 36 rev/h ( 2 π rev ) ( 1 h 3 , 600 sec ) = 0.062832 rad/s Calculate the moment of inertia ( I x ) about x axis: I x = m k x 2 Substitute 2500 kg for m and 0.9 m for k x . I x = 2500 × ( 0.9 ) 2 = 2025 kg ⋅ m 2 Calculate the moment of inertia I y about y axis: I y = m k y 2 Substitute 2,500 kg for m and 0.98 m for k y . I y = 2500 × ( 0.98 ) 2 = 2401 kg ⋅ m 2 Calculate the moment of inertia I z about z axis: I z = I x = 2025 kg ⋅ m 2 Calculate the initial angular moment ( H G ) 0 of the system about the mass centre. ( H G ) 0 = I y ω 0 j Substitute 0.062832 rad/s for ω 0 and 2401 kg ⋅ m 2 for I y . ( H G ) 0 = 2401 × 0.062832 j = ( 150.86 kg ⋅ m 2 / s ) j Show the distance a and b as in Figure (1). Calculate the value of ( a ) in Figure (1): a = B 2 Substitute 1.2 m for B . a = 1.2 2 = 0.6 m Calculate the value of ( b ) in Figure (1): b = a + B cos 45 ° Substitute 1.2 m for B and 0.6 m for a . b = 0.6 + 1.2 cos 45 ° = 1.4485 m Calculate the moment ( M G ) about the mass centre: M G = − b ( F A + F B ) i Substitute 1.4485 m for b and 20 N for F A and F B . M G = − 1.4485 ( 20 + 20 ) i = − ( 57.941 N ⋅ m ) i Calculate the angular moment ( H G ) of the system after 2 sec about the mass centre. H G = ( H G ) 0 + M G ( Δ t ) Substitute − ( 57.941 N ⋅ m ) i for M G , 2 sec for Δ t and ( 150.86 kg ⋅ m 2 / s ) j for ( H G ) 0 (b) To determine The rate ( φ ˙ ) of precession. (c) To determine The rate ( ψ ˙ ) of spin.

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 18, Problem 18.155RP

(a)

To determine

The precession axis of the satellite.

(b)

To determine

The rate (φ˙) of precession.

(c)

To determine

The rate (ψ˙) of spin.

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Chapter 18, Problem 18.154RP

Chapter 18, Problem 18.156RP

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The precession axis of the satellite.

Solution Summary: The author explains the satellite's precession axis, the radii of gyration, and the thrusters.

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The precession axis of the satellite.

The rate (φ˙) of precession.

The rate (ψ˙) of spin.

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Chapter 18 Solutions