Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-12T15:38:17.400Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Integration of Nearly-Hamiltonian Systems

Published online by Cambridge University Press:  12 April 2016

Victor R. Bond
Victor R. Bond*
Affiliation:
NASA – JSC, Houston, Texas, U.S.A.

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consideration is given to the solution by numerical integration of systems of differential equations that are derived from a Hamiltonian function in the extended phase space plus additional forces not included in the Hamiltonian (that is, nearly-Hamiltonian systems). An extended phase space Hamiltonian which vanishes initially will vanish on any solution of the system differential equations. Furthermore, it vanishes in spite of the additional forces, and defines a surface in the extended phase space upon which the solution is constrained.

Type
Part III. Numerical and Other Techniques
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 159 - 173
Copyright
Copyright © Reidel 1978

References

Baumgarte, J.: 1972, Celestial Mechanics 5, 490–501.CrossRefGoogle Scholar
Bettis, D.: 1970, Celestial Mechanics 2, 282–295.CrossRefGoogle Scholar
Bond, V. R.: 1976, Celestial Mechanics 13, 287–311.CrossRefGoogle Scholar
Cesari, L.: 1971, Asymptotic Behavior and Stability Problems in Ordinary Differential, Equations, Springer-Verlag, New York, Heidelberg, Berlin.CrossRefGoogle Scholar
Graf, O. and Bettis, D.: 1975, Celestial Mechanics 11, 433–448.CrossRefGoogle Scholar
Janin, G.: 1974, Celestial Mechanics 10, 451–467.CrossRefGoogle Scholar
Murdock, J.: 1975, Int. J. of Non-Linear Mechanics, 10, 259–270.CrossRefGoogle Scholar
Nacozy, P. E.: 1971, Astrophysics and Space Sci. 14, 40–51.CrossRefGoogle Scholar
Scheifele, G. and Graf, O.: 1974, AIAA Paper No. 74–838.Google Scholar
Shampine, L. F. and Gordon, M. K.: 1975, Computer Solution of Ordinary Differential Equations, Freeman, W. H., San Francisco.Google Scholar
Stiefel, E. and Scheifele, G.: 1971, Linear and Regular Celestial Mechanics, Springer, Berlin-Heidelberg-New York.CrossRefGoogle Scholar
Szebehely, V.: 1967, Theory of Orbits, Academic Press, N. Y. Google Scholar
Szebehely, V. and Bettis, D.: 1971, Astrophysics and Space Sci. 13, 365–376.CrossRefGoogle Scholar
Velez, C.: 1974, Celestial Mechanics 10, 405–422.CrossRefGoogle Scholar
Graf, O.: 1975, Johnson Space Center publication JSC Internal Note No. 75-FM-47.Google Scholar