Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T07:35:36.393Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of aircraft program motion with application to circular loop simulation

Published online by Cambridge University Press:  04 July 2016

W. Blajer
W. Blajer*
Affiliation:
Department of Mechanics, Technical University of Radom, Poland
Get access Rights & Permissions [Opens in a new window]

Summary

The objective of this paper is to present the principles of a mathematical model of aircraft prescribed motion. Requirements imposed on the aircraft motion are treated as program constraints on the system and both the transient dynamic solution of motion equations and the control ensuring the exact realisation of the prescribed motion are obtained as a result. The approach used is equivalent to the Lagrange multiplier method, generalised for the purpose of this paper. It consists of the solution of the set of differential/algebraic equations of index exceeding three. The presented mathematical model has been applied to the simulation of aircraft prescribed motion in a loop. The flight along an ideal circle and the flight with additionally demanded constant velocity are described. Some results of numerical calculations are demonstrated.

Type
Research Article
Information
The Aeronautical Journal , Volume 92 , Issue 917 , September 1988 , pp. 289 - 296
Copyright
Copyright © Royal Aeronautical Society 1988 

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. Duke, E. L. and Jones, F. P. Computer control for automated flight test manoeuvring, J Aircr, October 1984, 21, (10), 776–782.Google Scholar
2. Walker, R. A., Gupta, N. K., Duke, E. L. and Patterson, B. Developments in flight test trajectory control, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, AIAA-B4-0240, January 1984.Google Scholar
3. Sanh, Do. On the motion of controlled mechanical systems, Adv Mech, 1984, 7, (2), 3–24.Google Scholar
4. Krutko, P. D. Inverted problems in dynamics of controlled systems, Nauka, Moscow 1987 (in Russian).Google Scholar
5. Wittenburg, J. Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart 1977.Google Scholar
6. Hemami, H. and Weimer, F. C. Modelling of nonholonomic dynamic systems with applications. J Appl Mech, March 1981, 103, (1), 177–182.Google Scholar
7. Kamman, J. W. and Huston, R. L. Dynamics of constrained multibody systems, J Appl Mech. December 1984, 106, 899–903.Google Scholar
8. Arnold, V. I. Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin-Heidelberg-New York, 1978.Google Scholar
9. Etkin, B. Dynamics of Atmospheric Flight, John Wiley and Sons, New York-London-Sydney-Toronto, 1972.Google Scholar
10. Kane, T. R. and Levinson, D. A. Formulation of equation of motion for complex spacecraft, J Guid Contr, March-April 1980, 3, (2), 99–112.Google Scholar
11. Thomas, H. H. B. M. Some thoughts on mathematical models for flight dynamics, Aeronaut J, May 1984, 88, (875), 169–184.Google Scholar
12. Lötstedt, P. and Petzold, L. Numerical solution of nonlinear differential equations with algebraic constraints I: convergence results for differentiation formulas. Math Comput, April 1986, 46, (174), 491–516.Google Scholar
13. Gear, C. W. and Petzold, L. ODE methods for the solution of differential/algebraic systems, SIAM, J Numer Anal, August 1984, 21, (4), 716–728.Google Scholar
14. Korn, G. A. and Korn, T. M. Mathematical handbook for scientists and engineers, McGraw- Hill Book Co, New York-San Francisco-Toronto-London-Sydney, 1968.Google Scholar
15. Blajer, W. Numerical simulation of airplane program motion in vertical loop, (in Polish), Theor Appl Mech, 1987, 25, (4). 621–633.Google Scholar
16. Blajer, W. Modelling and control of systems with program constraints, AMSE Adv Model Simul, 1988, 12, (3), 53–63.Google Scholar