Stabilizing the explicit euler integration of stiff and undamped linear systems

Journal of Guidance, Control, and Dynamics

Volumn 30, Issue 6, 2007, Pages 1659-1667

  Gurfil, Pini ^a,b,c   Klein, Itzik ^a,b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b Faculty of Aerospace Engineering   (Israel)

^c AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EFFICIENCY; COVARIANCE MATRIX; EULER EQUATIONS; INTEGRATION; LINEAR SYSTEMS; MEASUREMENT ERRORS;

EULER INTEGRATION; NUMERICAL ERRORS; STATE VARIABLES;

NUMERICAL METHODS;

EID: 36849089119     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.29148     Document Type: Article

References (21)

1. Newton, I., Philosophiae Naturalis Principia Mathematica, Edmond Halley, London, 1687, Chap. 2, pp. 65-117.
2. Ball, W. W., A Short Account of the History of Mathematics, 4th ed., Dover, New York, 1960, Chap. 18, pp. 398-400.
3. Butcher, J. C., The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods, Wiley, New York, 1987, pp. 25-46, Chap. 2.
4. Ogata, K., Modern Control Engineering, 4th ed., Pearson Education International, Upper Saddle River, NJ, 2002, Chap. 3, pp. 53-58.
5. Cannon, R. H., Dynamics of Physical Systems, McGraw-Hill, New York, 1967, Chap. 2, pp. 32-57.
6. Bisplinghoff, R. L., Ashley, H., and Hlfman, R. L., Aeroelasticity, Dover, New York, 1996, Chap. 11, pp. 695-715.
7. Shinya, M., "Theories for Mass-Spring Simulation in Computer Graphics: Stability, Costs and Improvements," IEICE Transactions on information and Systems, Vol. E88-D, No. 4, Apr. 2005, pp. 767-774.
8. Euler, L., "Recherches sur la Question des Inegalites du Movement de Saturne et de Jupiter," Piece qui a Remporte le Prix, de l'Académie Royale des Sciences, Année, France, 1748.
9. Lagrange, J. L., "Sur la Theorie des Variations des Elements des Planetes et en Particulier des Variations des Grands Axes de Leurs Orbites," l'Institut de France, Paris, 1808.
10. Wanner, E. H. G., Solving Ordinary Differential Equations II- Stiff and Differential-Algebraic Problems, Springer, New York, 1996, pp. 15-37, Chap. 4.
11. Shieh, L., Mehio, M. M., and Dib, H. M., "Stability of the Second-Order Matrix Polynomial," IEEE Transactions on Automatic Control, Vol. AC-32, No. 3, 1987, pp. 231-233.
12. Bellman, R., Introduction to Matrix Analysis, McGraw-Hill, New York, 1970, pp. 10, 67.
13. Anderson, B., and Bitmead, R. E., "Stability of Matrix Polynomials," International Journal of Control, Vol. 26, No. 2, 1977, pp. 235-247.
14. Franklin, G. F., Digital Control of Dynamic Systems, Addison Wesley Longman, Reading, MA, 1998, Chap. 4, pp. 79-80.
15. Dahlquist, G., "Stability of Two-Step Methods for Variable Integration Steps," SIAM Journal on Numerical Analysis, Vol. 20, No. 5, 1983, pp. 1071-1085.
16. Horn, R. A., and Johnson, C., Matrix Analysis, Cambridge Univ. Press, Cambridge, England, U.K., 1985, pp. 7-12.
17. Boyce, W. E., and Diprima, R. C., Elementary Differential Equations, 6th ed., Wiley, New York, 1996, Chap. 4, pp. 237-242.
18. Gurfil, P., and Klein, I., "Mitigating the Integration Error in Numerical Simulations of Newtonian Systems," International Journal for Numerical Methods in Engineering, Vol. 68, No. 2, 2006, pp. 267-297.
19. Kwakernaak, H., and Sivan, R., Linear Optimal Control Systems, Wiley Interscience, New York, 1972, Chap. 1.
20. Wie, B., Space Vehicle Dynamics and Control, AIAA Education Series, AIAA, Reston, VA, 1998, Chap. 8, pp. 463-501.
21. Meirovitch, L., Introduction to Dynamics and Control, Wiley, New York, 1985, pp. 42-56.