By Hanspeter Schaub, John L. Junkins

This unmarried resource offers a finished remedy of dynamics of aerospace structures beginning with the fundamental basics. subject matters diversity from easy kinematics and dynamics to extra complex celestial mechanics. It publications you thru some of the derivations and proofs, yet avoids "cookbook" formulation. as a substitute, the reader is made to appreciate the underlying precept of the concerned equations and proven find out how to follow them to varied dynamical structures. The booklet is split into elements. half I covers analytical therapy of subject matters equivalent to easy dynamic rules as much as complex strength idea. particular consciousness is paid to using rotating reference frames that regularly take place in aerospace structures. half II covers simple celestial mechanics treating the 2-body challenge, limited 3-body challenge, gravity box modelling, perturbation tools, spacecraft formation flying, and orbit transfers.

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**Extra resources for Analytical Mechanics of Space Systems (AIAA Education)**

**Example text**

The relative position vector σ of the point mass to O and its inertial derivative are given by σ = leˆr σ˙ = lθ˙ eˆθ The angular momentum vector HO can then be written as HO = σ × mσ˙ = −ml2 θ˙ n ˆ3 and its inertial derivative is given by ˙ O = −ml2 θ¨n H ˆ3 The torque LO about point O is written as LO = σ × F g − R n ˆ 2 × (Ff + N ) = −mgl sin (θ + α) n ˆ 3 − RFf n ˆ3 The inertial position vector rO of point O and its second inertial derivative are given by rO = d n ˆ 1 = Rθn ˆ1 ˆ1 r¨O = Rθ¨n Euler’s equation with moments about a general point in Eq.

48), the equations of motion for the center of mass of the three-mass system is 4m¨ rc = 3f Assuming that the rc is originally at rest at the origin, the system center of mass location is then integrated to obtain 3f 2 t 8m To find the equations of motion of the individual masses, we need to write Eq. 39) for each mass. rc (t) = 2m¨ r1 = k(r2 − r1 ) m¨ r2 = −k(r2 − r1 ) + k(r3 − r2 ) + f m¨ r3 = −k(r3 − r2 ) + 2f This can be written in a standard ODE matrix form for a vibrating system 0 k −k 0 r1 r¨1 2m 0 0 0 m 0 r¨2 + −k 2k −k r2 = f 2f 0 −k k 0 0 m r3 r¨3 which can be solved given a set of initial conditions for ri (t0 ) and r˙i (t0 ).

Assume the sun is inertially fixed in space by the radius r at a constant rate θ. frame {n ˆ 1, n ˆ 2, n ˆ 3 }. Further, a UFO is orbiting the sun at a radius R2 at fixed rate γ. ˙ Let the Earth frame E be given by the direction vectors {ˆ er , eˆφ , eˆ3 }, the moon frame M by {m ˆ r, m ˆ 3 } and the UFO frame U by {u ˆ θ, m ˆr, u ˆγ , u ˆ 3 }. a) Find the inertial velocity and acceleration of the moon relative to the sun. b) Find the position vector of the moon relative to the UFO. c) Find the angular velocity vectors ωE/U and ωM/U .