Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T17:52:16.405Z Has data issue: false hasContentIssue false
  • English
  • Français

The Transformation of Aerodynamic Stability Derivatives by Symbolic Mathematical Computation

Published online by Cambridge University Press:  07 June 2016

James C Howard
James C Howard*
Affiliation:
NASA-Ames Research Center
Get access

Summary

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Type
Research Article
Information
Aeronautical Quarterly , Volume 26 , Issue 2 , May 1975 , pp. 109 - 116
Copyright
Copyright © Royal Aeronautical Society. 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Etkin, B Dynamics of Flight. Wiley, New York, p 116, p 495, 1959.Google Scholar
2 Sokolinikoff, I S Tensor Analysis, Theory and Applications. Wiley, New York, p 63, 1960.Google Scholar
3 Tobey, R G FORMAC interpreter user’s manual. IBM-Boston Programming Center, Cambridge, Mass’ 1967.Google Scholar
4 Howard, J C Application of computers to the formulation of problems in curvilinear coordinate systems. NASA Technical Note D-3939, 1967.Google Scholar
5 Howard, J C Automatic problem formulation using the metric properties of space. Journal of the Franklin Institute, Vol 29, No 6, pp 535–543, 1971.CrossRefGoogle Scholar
6 Patten, J S Jr A FORMAC algorithm for generating equations of motion for a general system of rigid bodies. Proceedings of SHARE XXXVII Symbolic Mathematical Computation Project, New York, August 1971.Google Scholar
7 Howard, J C Computer formulation of the equations of motion using tensor notation. Communications of the Association for Computing Machinery, Vol 10, No 9; pp 543–548, 1967.CrossRefGoogle Scholar
8 Howard, J C An algorithm for deriving the equations of mathematical physics by symbolic manipulation. Communications of the Association for Computing Machinery, Vol 11, No 12, 1968.CrossRefGoogle Scholar
9 Howard, J C The application of symbolic mathematical computation to the formulation of models of diverse phenomena. Proceedings of SHARE XXXVIII Meeting, San Francisco, March 1972.Google Scholar
10 Howard, J C Mathematical modeling by symbolic mathematical computation — A cosmological application. NASA Technical Note D-6233, 1971.Google Scholar
11 McConnell, A J Applications of Tensor Analysis. Dover Publications, New York, p 22, 1957.Google Scholar
12 Gainer, T G Hoffman, S Summary of transformation equations and equations of motion used in free-flight and wind-tunnel data reduction and analysis. NASA SP-3070, 1972.Google Scholar