Applied cartesian tensors for aerospace simulations
American Institute of Aeronautics and Astronautics, 2006 - Mathematics - 215 pages
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 in use today and that are 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 multi-variable 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.
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Motion of a Point Mass in Gravitational Space
JVBody Gravitational Space and Rigid Body Motion
Flight Vehicle Motion
4 other sections not shown
acceleration Aerospace Applications aircraft airframe airplane analysis angle of attack angular momentum astrodynamics attitude axis rotation rates becomes body axis coordinates body axis rotation Cartesian Cartesian tensor center of mass contact forces coordinate axes coordinate axis coordinate center defined derived differential equations discussed in Sec dot product drag forces dynamics Earth epoch equations of motion estimated Euler angle Euler angle set Euler rotation flight vehicle follows forces acting function given in Eq gravitational space inertial coordinate frame inertial frame inertial space integral lifting surface LVLH coordinate mass particles mean orbital elements notation numerical onboard orbital elements orbital plane parameters perturbing point mass pressure quaternion rate of change relationship relative motion rigid body rocket engine Rotation Sequence S2 cos S3 semimajor axis shown in Fig simply space vehicle station coordinate subbody summation term torques trajectory transformation matrix true anomaly vector components vehicle's velocity vector zero