Space Flight Dynamics by Craig A. Kluever | 9781119157823 | 111915782X | Holooly

Mechanics of Flight

Space Flight Dynamics

87 SOLVED PROBLEMS

Question: 13.3

The DC motor associated with the reaction wheel and spacecraft from Example 13.2 has the following parameters: motor torque constant Km = 0.043 N-m/A, back-emf constant Kb = 0.043 V-s/rad, resistance R = 2.8 Ω, and friction coefficient b = 6(10^–5) N-m-s/rad. Determine the input voltage to the DC ...

Verified Answer:

We can manipulate Eq. (13.40)

T_{m}={\frac{...

Question: 13.2

Satellite operators want to accurately determine a spacecraft’s principal moment of inertia after it has fired an onboard rocket and expended propellant mass. The spacecraft is equipped with a reaction wheel, and both the spacecraft and wheel are initially at rest (i.e., zero angular momentum). The ...

Verified Answer:

Because the satellite and wheel are initially at r...

Question: 12.6

Suppose GEOSAT (shown in Figure 12.24) has principal moments of inertia I3 = 100 kg-m² (long minor axis) and I1 = I2 = 2,600 kg-m² (transverse major axes). If GEOSAT operated in an 800-km altitude circular orbit, compute the frequency and period of the pitch libration motion caused by the ...

Verified Answer:

Equation (12.130) provides the libration frequency...

Question: 12.5

An axisymmetric oblate satellite has principal moments of inertia I3 = 1,100 kg-m² (major axis) and I1 = I2 = 700 kg-m² (minor axes). At time t = 0, the satellite has the angular velocity vector (in body-fixed coordinates) ω0 = −0 2u1 + 0 1u2 + 8 3u3 rad/s The satellite is equipped with a nutation ...

Verified Answer:

a) First, let us compute the angular momentum vect...

Question: 12.4

The approximate mass properties of the Explorer 1 satellite are Mass: m = 14 kg Minor-axis moment of inertia: I3 = 0.17 kg-m² Major-axis moment of inertia: I1 = I2 = 5 kg-m² Initially Explorer 1 was spinning at 750 rpm (ω0 = 78.54 rad/s) about its minor axis. Determine the initial and final ...

Verified Answer:

We use Eq. (12.89) to determine the initial kineti...

Question: 12.2

The Intelsat II series of communication satellites were deployed in geostationary-equatorial orbit (GEO) in the late 1960s. Intelsat II was an oblate cylinder with a diameter of 1.42 m and height of 0.67 m. Before firing the apogee rocket engine for insertion into GEO, the Intelsat II was spun ...

Verified Answer:

a) We know that angular momentum is

\mathbf...

Question: 12.1

Consider the two cylindrically shaped satellites shown in Figure 12.5. Figure 12.5a shows a symmetrical satellite with homogeneous mass distribution, whereas Figure 12.5b shows an asymmetrical cylinder that is “unbalanced” due to the 50-kg mass m1 offset from the origin. The offset distances for m1 ...

Verified Answer:

We will consider the symmetrical satellite in Figu...

Question: 11.7

For the final entry-heating example, consider again the winged vehicle and entry conditions from Example 11.3. Compute the ratio of peak heating rates for an equilibrium glide and skip entry. Because the winged vehicle has relatively high L/D (=1.5), let the constant bank angle be ϕ = 60° for the ...

Verified Answer:

Recall that the vehicle's ballistic coefficient is...

Question: 11.6

Using the vehicle data and entry conditions from Example 11.3, determine the critical flight-path angle, altitude, and velocity corresponding to the peak aerodynamic heating rate for a skip entry. ...

Verified Answer:

The winged entry vehicle in Example 11.3 has [late...

Question: 11.5

Using the Space Shuttle vehicle data and entry conditions in Example 11.2, determine the critical altitude and velocity for peak aerodynamic heating rate for an equilibrium glide. ...

Verified Answer:

We determined the Shuttle's ballistic coefficient ...

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