《A Mathematical Perspective on Flight Dynamics and Control》
《A Mathematical Perspective on Flight Dynamics and Control》在飞行动力学与控制的数学观点
作者:
Andrea L’Afflitto
School of Aerospace and Mechanical
Engineering
The University of Oklahoma
出版社:Springer
出版时间:2017年
目录
1 Fundamentals of Rigid Body Dynamics . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vectors and Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 The First Derivative of a Vector with Respect to Time . . . . . . . . 5
1.4 Tait–Bryan Angles and Rotations . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 Tait–Bryan Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 Rotations of Reference Frames and Vectors. . . . . . . . . . . 12
1.4.3 Properties of the Tait–Bryan Angles
and Rotation Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Euler Parameters, Quaternions, and Rotations . . . . . . . . . . . . . . 19
1.5.1 Quaternions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Quaternions and Rotations . . . . . . . . . . . . . . . . . . . . . . 23
1.5.3 Euler Parameters and Angular Velocity. . . . . . . . . . . . . . 26
1.6 The Second Derivative of a Vector with Respect to Time . . . . . . 28
1.7 Equations of Motion of a Rigid Body. . . . . . . . . . . . . . . . . . . . 30
2 Equations of Motion of an Aircraft . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.1 Body and Inertial Reference Frames . . . . . . . . . . . . . . . . 35
2.1.2 The Aircraft State Vector . . . . . . . . . . . . . . . . . . . . . . . 37
2.1.3 The Aircraft Control Vector . . . . . . . . . . . . . . . . . . . . . 37
2.1.4 Aerodynamic Angles . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Forces and Moments Acting on an Aircraft . . . . . . . . . . . . . . . . 41
2.3 Equations of Motion of an Aircraft. . . . . . . . . . . . . . . . . . . . . . 42
2.4 Flight at Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5 Linearization of the Aircraft Equations of Motion. . . . . . . . . . . . 46
2.6 Decoupling of the Linearized Equations of Motion. . . . . . . . . . . 48
2.7 Analysis of the Longitudinal Dynamics of an Aircraft. . . . . . . . . 54
2.8 Analysis of the Lateral-Directional Dynamics of an Aircraft . . . . 59
xi
3 Aircraft Automatic Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3 Proportional-Integral-Derivative Control . . . . . . . . . . . . . . . . . . 67
3.4 The Linear-Quadratic Gaussian Control. . . . . . . . . . . . . . . . . . . 75
3.5 Optimal State-Feedback H1 control . . . . . . . . . . . . . . . . . . . . . 81
3.6 Model Reference Adaptive Control. . . . . . . . . . . . . . . . . . . . . . 84
4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Appendix A: Fundamentals of Dynamical Systems Theory . . . . . . . . . 91
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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