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.
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)
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.