Abstract
We study the linear stability of the triangular points in the elliptic restricted problem by determining the characteristic exponents with a convergent method of iteration which in essence was introduced by Cesari (1940). We obtain the general term of such exponents as a power series in the eccentricity ε of the primaries, valid for sufficiently small ε and at all values of μ except one in the interval of stability of the circular problem.
Similar content being viewed by others
References
Breakwell, J. V. and Pringle, R.: 1966,Progress in Astronautics and Aeronautics: Methods in Astrodynamics and Celestial Mechanics, (ed. by V. Szebehely and R. Duncombe), Vol. 17 Academic Press, New York.
Cesari, L.: 1940,Mem. Accad. Ital. Cl. Sci. Fis. Mat. Nat. 11, 633.
Cesari, L.: 1962,Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, 2nd ed., Springer-Verlag, Berlin (published by Academic Press, New York).
Danby, J. M. A.: 1964,Astron. J. 69, 165.
Deprit, A. and Rom, A.: 1970,Astron. Astrophys. 5, 416.
Gambill, R. A.: 1954,Riv. Mat. Univ. Parma 5, 169.
Gambill, R. A.: 1955,Riv. Mat. Univ. Parma 6, 37.
Gambill, R. A.: 1956,Riv. Mat. Univ. Parma 7, 311.
Hale, J. K.: 1954,Riv. Mat. Univ. Parma 5, 137.
Hale, J. K.: 1963,Nonlinear Oscillations, McGraw-Hill, New York.
Szebehely, V.: 1966,Theory of Orbits, Acad. Press, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Giacaglia, G.E.O. Characteristic exponents atL 4 andL 5 in the elliptic restricted problem of three bodies. Celestial Mechanics 4, 468–489 (1971). https://doi.org/10.1007/BF01231404
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01231404