Applied cartesian tensors for aerospace simulations / David M. Henderson.

Format:

Book

Author/Creator:

Henderson, David M. (David Melvin), 1935-

Contributor:

Alumni and Friends Memorial Book Fund.

John G. Hartman Memorial Library Fund.

Series:

AIAA education series

Language:

English

Subjects (All):

Flight simulators--Mathematics.

Flight simulators.

Calculus of tensors.

Mathematics.

Physical Description:

xiii, 215 pages : illustrations ; 23 cm.

Place of Publication:

Reston, Va. : American Institute of Aeronautics and Astronautics, 2006.

Summary:

This book presents a new approach to aerospace flight vehicle equations of motion based on a unifying tensor-based formulation. Covering the fundamental concepts of the geometry of space, applied mechanics, and aerospace engineering analysis, the author builds on these flight mechanics essentials to describe the motion of aircraft and space vehicles. Concepts are amplified by the presentation of aerospace applications that are in use today and tied directly to the material presented.

The basic concepts of Cartesian analysis are developed, along with the application of tensor notation to engineering analysis. Tensor notation (the Einstein summation convention) is introduced to give the reader exact component equations and to demonstrate its value in multivariable analysis.

By applying the summation notation in the analysis, the author believes that a more complete description of the dynamic problems of aerospace vehicle motion can be offered, and that this approach is already finding applications in aerospace engineering technologies.

Contents:

Chapter 1 Geometric Concepts in the Absence of Mass and Gravitation 1

1.1 Position Transformation 2

1.2 Properties of the Transformation Matrix 9

1.3 Euler Angles and the Transformation Matrix 18

1.4 Euler's Theorem and Four Parameter Methods 27

1.5 Differentiation of the Transformation Matrix 41

1.6 Transformation Equations for Velocity and Acceleration 52

Chapter 2 Motion of a Point Mass in Gravitational Space 59

2.1 Point Mass: Mathematical Descriptions 60

2.2 Point Mass and Gravitation 66

2.3 Point Mass Motion Relative to Earth-Based Coordinates 82

2.4 Point Mass Motion Relative to Space-Based Coordinates 94

Chapter 3 N-Body Gravitational Space and Rigid Body Motion 107

3.1 N-Body Mass Systems: Mathematical Descriptions 107

3.2 Rigid Body Dynamics 120

Chapter 4 Flight Vehicle Motion 129

4.1 Modeling Gravitational Environments for Aerospace Vehicles 130

4.2 Forces and Moments on the Flight Vehicle 139

4.3 Flight Vehicle Motion Simulations 171

4.4 Space Vehicle Motion Using Mean Orbital Elements 176

Appendix A Relationships for Three-Axis Euler Rotational Sequences 187

Appendix B C-W State Transition Matrix for LVLH Relative Motion 195

Appendix C Integral Lists for Computer Simulation Algorithms 197

Appendix D Numerical Solution Methods for Differential Equations: Computer Simulation Algorithms 201.

Notes:

Includes bibliographical references (pages 205-208) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the John G. Hartman Memorial Library Fund.

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

1563477939

OCLC:

62896379