By Hanspeter Schaub, John L. Junkins
This unmarried resource presents a accomplished remedy of dynamics of aerospace structures beginning with the fundamental basics. issues variety from uncomplicated kinematics and dynamics to extra complicated celestial mechanics. It publications you thru a number 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 the best way to practice them to varied dynamical platforms. The publication is split into elements. half I covers analytical therapy of issues corresponding to simple dynamic ideas as much as complicated power idea. specific recognition is paid to using rotating reference frames that regularly ensue in aerospace platforms. 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 info for Analytical Mechanics of Space Systems (AIAA Education)
2. As can be verified, the special case where x ˜1 = 0 gives x ˜2 = v02 /2g. You can readily show that this is the apogee of a vertically launched projectile with launch velocity v0 . Another special case where is where x ˜2 = 0, which provides the maximum impact range x1 = v02 /g if the surface is flat. 3 compares the various launch angles required to hit a target a distance x1 away with a given initial velocity v02 . For this constant gravity field case, the maximum range launch angle is always 45 degrees.
80) B After substituting Eq. 75) we obtain the equivalent super particle theorem for a continuous body. 81) Kinetic Energy Let the inertial vector R define the position of the infinitesimal mass element dm. 83) Making use of Eqs. 84) The first term in Eq. 84) represents the translational kinetic energy and the second the rotational and deformational energy. To find the work done on the continuous body B the kinetic energy rate is found. 85) ¨ −R ¨ c the kinetic energy rate is After using Eq. 86) B Using Eqs.
2 Kinetic Energy The total kinetic energy T of the cloud of N particles can be written as the sum of the kinetic energies of each particle. 50) 42 NEWTONIAN MECHANICS CHAPTER 2 where the middle term N i=1 mi r˙ i is zero due to the definition of the center of mass in Eq. 43). 51) where the first term contains the system translational kinetic energy and the second contains the system rotation and deformation kinetic energy. To find the work done on the system we examine the energy rate dT /dt. 53) i=1 After using Eqs.
Analytical Mechanics of Space Systems (AIAA Education) by Hanspeter Schaub, John L. Junkins