Atmospheric and Space Flight Dynamics: Modeling and by Ashish Tewari

By Ashish Tewari

This publication deals a unified presentation that doesn't discriminate among atmospheric and house flight. It demonstrates that the 2 disciplines have advanced from an analogous set of actual ideas and introduces a large variety of severe strategies in an available, but mathematically rigorous presentation.

The e-book provides many MATLAB and Simulink-based numerical examples and real-world simulations. Replete with illustrations, end-of-chapter routines, and chosen strategies, the paintings is essentially helpful as a textbook for complicated undergraduate and starting graduate-level students.

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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)

Example text

86) 38 2 Attitude and Kinematics of Coordinate Frames Therefore, the time derivative of the quaternion is the following: d{q, q4 }T . {q(t + Δt), q4 (t + Δt)}T − {q(t), q4 (t)}T = lim Δt→0 dt Δt 1 = Ω{q(t), q4 (t)}T . 87) The linear, algebraic form of the matrix differential equation, Eq. 87), is an obvious advantage of the quaternion representation. Unlike the Euler angles, it is not required to evaluate trigonometric functions in the process of solving the kinematic equations. The matrix Ω is either constant, or timevarying, depending upon whether the components of the angular velocity are changing with time.

In such a case, the axes of the rotating coordinate frame are fixed to the rigid body and can be used to represent the attitude and angular velocity of the body relative to an inertial (or space-fixed) frame. On rare occasions, it is desired to alternatively express the angular velocity with components along the axes of an inertial frame. In such a case the angular velocity is termed space-referenced, or inertial angular velocity, and is related to the body referenced angular velocity by ωI = CT (t)ω(t) according to the coordinate transformation of Eq.

S(a) = ⎝ a3 −a2 a1 0 A skew-symmetric matrix has the property S(a)T = −S(a). 2. Find the Euler angles from the elements of the rotation matrix for the representation (ψ)3 , (θ)1 , (φ)3 . What are the points of singularity for this representation? 3. Derive the general expressions for the Euler axis, e, and the principal angle, Φ, in terms of a symmetric Euler angle representation. Can such simple expressions be obtained for an asymmetric set? 4. The singularity of an Euler angle representation prevents the Euler angles from describing infinitesimal rotations about singular orientations.

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