By Ashish Tewari

This e-book bargains a unified presentation that doesn't discriminate among atmospheric and area flight. It demonstrates that the 2 disciplines have developed from an identical set of actual ideas and introduces a huge diversity of serious ideas 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 options, the paintings is basically valuable as a textbook for complex undergraduate and starting graduate-level students.

**Read 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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**Additional resources for Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB® and Simulink® (Modeling and Simulation in Science, Engineering and Technology)**

**Sample text**

7 Rodrigues Parameters (Gibbs Vector) A set of three attitude parameters, ρ = (ρ1 , ρ2 , ρ3 )T , called Rodrigues parameters, or the Gibbs vector, can be directly derived from the quaternion (q, q4 ) as follows: 28 2 Attitude and Kinematics of Coordinate Frames . 55) which, when substituted into Eq. 44), yields ρ = e tan Φ . 56) The composition rule for Rodrigues parameters can be derived from that for the quaternion [Eq. 57) where ρ represents the ﬁnal orientation obtained by combining ρ and ρ .

Euler’s theorem thus provides an alternative description of rotation using unit vector, e, representing the direction of Euler axis, and the principal rotation angle, Φ. Before using the new representation, we must know how these two quantities can be derived. An insight into the Euler axis can be obtained by analyzing the eigenvalues and eigenvectors [4] of the rotation matrix. Let c be an eigenvector associated with the eigenvalue, λ of C: Cc = λc . 26) By premultiplying Eq. 27) (Cc)H (Cc) = λλcH c , or, since C is real and satisﬁes Eq.

1. m for Deriving the Quaternion from Rotation Matrix function q=quaternion(C) %(c) 2006 Ashish Tewari T=trace(C); qsq=[1+2*C(1,1)-T;1+2*C(2,2)-T;1+2*C(3,3)-T;1+T]/4; [x,i]=max(qsq); if i==4 q(4)=sqrt(x); q(1)=(C(2,3)-C(3,2))/(4*q(4)); q(2)=(C(3,1)-C(1,3))/(4*q(4)); q(3)=(C(1,2)-C(2,1))/(4*q(4)); end if i==3 q(3)=sqrt(x); q(1)=(C(1,3)+C(3,1))/(4*q(3)); q(2)=(C(3,2)+C(2,3))/(4*q(3)); q(4)=(C(1,2)-C(2,1))/(4*q(3)); end if i==2 q(2)=sqrt(x); q(1)=(C(1,2)+C(2,1))/(4*q(2)); q(3)=(C(3,2)+C(2,3))/(4*q(2)); q(4)=(C(3,1)-C(1,3))/(4*q(2)); end if i==1 q(1)=sqrt(x); q(2)=(C(1,2)+C(2,1))/(4*q(1)); q(3)=(C(1,3)+C(3,1))/(4*q(1)); q(4)=(C(2,3)-C(3,2))/(4*q(1)); end eﬃciency of the quaternion relationship, Eq.