Download Atmospheric and Space Flight Dynamics: Modeling and by Ashish Tewari PDF

By Ashish Tewari

This e-book bargains a unified presentation that doesn't discriminate among atmospheric and house flight. It demonstrates that the 2 disciplines have developed from a similar set of actual ideas and introduces a huge variety of severe techniques in an obtainable, but mathematically rigorous presentation.

The booklet provides many MATLAB and Simulink-based numerical examples and real-world simulations. Replete with illustrations, end-of-chapter workouts, and chosen recommendations, the paintings is basically beneficial as a textbook for complex undergraduate and starting graduate-level students.

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Read Online or Download Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB® and Simulink® (Modeling and Simulation in Science, Engineering and Technology) PDF

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Extra info for Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB® and Simulink® (Modeling and Simulation in Science, Engineering and Technology)

Example text

The singularity of an Euler angle representation prevents the Euler angles from describing infinitesimal rotations about singular orientations. Using the representation (ψ)3 , (θ)1 , (φ)3 , show that if an infinitesimal rotation is performed about OY from the initial orientation of φ = θ = ψ = 0, the Euler angles change instantaneously to finite values. 5. 1) formed out of the elements of e: ⎞ ⎛ 0 −e3 e2 0 −e1 ⎠ . S(e) = ⎝ e3 −e2 e1 0 This relationship between the rotation matrix and principal rotation angle/Euler axis is called Euler’s formula.

M-file rotquat for the Computation of Rotation Matrix from the Quaternion function C=rotquat(q) % rotation matrix from the quaternion % (c) 2006 Ashish Tewari S=[0 -q(3,1) q(2,1);q(3,1) 0 -q(1,1);-q(2,1) q(1,1) 0]; C=(q(4,1)^2-q(1:3,1)’*q(1:3,1))*eye(3)+2*q(1:3,1)*q(1:3,1)’-2*q(4,1)*S; Finally, we consider the kinematical representation possible through the modified Rodrigues parameters, p = (p1 , p2 , p3 )T . Being a minimal representation based upon the quaternion, p, reduces the number of kinematic, first-order differential equations required by the latter.

Using the representation (ψ)3 , (θ)1 , (φ)3 , show that if an infinitesimal rotation is performed about OY from the initial orientation of φ = θ = ψ = 0, the Euler angles change instantaneously to finite values. 5. 1) formed out of the elements of e: ⎞ ⎛ 0 −e3 e2 0 −e1 ⎠ . S(e) = ⎝ e3 −e2 e1 0 This relationship between the rotation matrix and principal rotation angle/Euler axis is called Euler’s formula. 6. Derive Eq. 5 and the definition of the quaternion given in Eq. 44). Note the similarity in the form of E and Q.

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