Secular perturbation theory and computation of asteroid proper elements

1990 ◽  
Vol 49 (4) ◽  
pp. 347-411 ◽  
Author(s):  
Andrea Milani ◽  
Zoran Knežević
Keyword(s):  
Perturbation Theory ◽  
Secular Perturbation ◽  
Proper Elements

scholarly journals Stability Mechanism of Planetary System of ν Andromedae

2004 ◽  
Vol 202 ◽  
pp. 202-204 ◽  
Author(s):  
Hiroshi Kinoshita ◽  
Hiroshi Nakai
Keyword(s):  
Perturbation Theory ◽  
Planetary System ◽  
Secular Resonance ◽  
Secular Perturbation ◽  
Outer Planets ◽  
The Stability

Three planets are detected around ν Andromedae. The stability of Upsilon Andromedae Planetary system is maintained by the co rotation of the pericenters of the two outer planets. If the pericenters of the two outer planets move independently, the planetary system becomes unstable. The corotation of the pericenters is explained by the secular perturbation theory. This corotation is not a secular resonance.

scholarly journals On the divergence difficulty of quantized field theories and the rigorous treatment of radiation reaction

1946 ◽  
Vol 186 (1004) ◽  
pp. 119-147 ◽  
Keyword(s):  
Perturbation Theory ◽  
Expansion Method ◽  
Radiation Reaction ◽  
Field Theories ◽  
Unperturbed System ◽  
Secular Perturbation ◽  
Rigorous Treatment ◽  
Quantized Field

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown th at the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty, in certain cases, disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, this amounts to a rigorous treatm ent of the radiation reaction, in such cases where its effect is strong.

scholarly journals The Locations of Secular Resonances and the Evolution of Small Solar System Bodies

1992 ◽  
Vol 152 ◽  
pp. 123-132
Author(s):  
Ch Froeschle ◽  
P. Farinella ◽  
C. Froeschle ◽  
Z. Knežević ◽  
A. Milani
Keyword(s):  
Perturbation Theory ◽  
Solar System ◽  
Small Body ◽  
Kuiper Belt ◽  
Dynamical Evolution ◽  
Asteroid Belt ◽  
Secular Resonances ◽  
Outer Planets ◽  
Proper Elements ◽  
Solar System Bodies

Generalizing the secular perturbation theory of Milani and Knežević (1990), we have determined in the a — e — I proper elements space the locations of the secular resonances between the precession rates of the longitudes of perihelion and node of a small body and the corresponding eigenfrequencies of the secular perturbations of the four outer planets. We discuss some implications of the results for the dynamical evolution of small solar system bodies. In particular, our findings include: (i) the fact that the g = g6 resonance in the inner asteroid belt lies closer than previously assumed to the Flora region, providing a plausible dynamical route to inject asteroid fragments into planet-crossing orbits; (ii) the possible presence of some low-inclination “stable islands” between the orbits of the outer planets; (iii) the fact that none of the secular resonances considered in this work exists for semimajor axes > 50 AU, so that these resonances do not provide a mechanism for transporting inwards possible Kuiper–belt comets.

scholarly journals The spring oscillator model degenerated into the coupled-mode theory by using secular perturbation theory

2020 ◽  
Vol 69 (7) ◽  
pp. 074501
Author(s):  
Cun-Yuan Zhu ◽  
Chao-Gang Li ◽  
Quan Fang ◽  
Mao-Sheng Wang ◽  
Xue-Cheng Peng ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Oscillator Model ◽  
Coupled Mode Theory ◽  
Secular Perturbation ◽  
Mode Theory ◽  
Coupled Mode

scholarly journals On the Ages of Asteroid Families

1983 ◽  
Vol 74 ◽  
pp. 203-210
Author(s):  
Manabu Yuasa
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Secular Perturbation ◽  
Asteroid Families

The ages of asteroid families are estimated by using a second order secular perturbation theory. Their ages are rather young. To explain these results we have some possible interpretations. The first interpretation is that in the theory of secular perturbation we do not include the effects of mutual perturbations of asteroids. The second is that we can regard these values as the minimum ages.

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