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Analytical and numerical results on the positivity of steady state solutions of a thin film equation
The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities
1. | Dipartimento di Matematica, Universitá di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy |
2. | Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy |
References:
[1] |
V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, "Mathematical Aspects of Classical and Celestial Mechanics," Springer, 1997. |
[2] |
R. V. Baluyev and K. V. Kholshevnikov, Distance between Two Arbitrary Unperturbed Orbits, Cel. Mech. Dyn. Ast., 91 (2005), 287-300.
doi: 10.1007/s10569-004-3207-1. |
[3] |
E. Bowell and K. Muinonen, Earth-crossing asteroids and comets: Groundbased search strategies, in "Hazards due to Comets & Asteroids" (Ed. T. Gehrels), Tucson: The University of Arizona Press, (1994), 149-197. |
[4] |
R. A. Broucke and P. J. Cefola, On the equinoctial orbit elements, Cel. Mech. Dyn. Ast., 5 (1972), 303-310. |
[5] |
G. F. Gronchi, Generalized averaging principle and the secular evolution of planet crossing orbits, Cel. Mech. Dyn. Ast., 83 (2002), 97-120.
doi: 10.1023/A:1020178613365. |
[6] |
G. F. Gronchi, On the stationary points of the squared distance between two ellipses with a common focus, SIAM Journ. Sci. Comp., 24 (2002), 61-80.
doi: 10.1137/S1064827500374170. |
[7] |
G. F. Gronchi, An algebraic method to compute the critical points of the distance function between two Keplerian orbits, Cel. Mech. Dyn. Ast., 93 (2005), 297-332.
doi: 10.1007/s10569-005-1623-5. |
[8] |
G. F. Gronchi and A. Milani, Averaging on Earth-crossing orbits, Cel. Mech. Dyn. Ast., 71 (1998), 109-136.
doi: 10.1023/A:1008315321603. |
[9] |
G. F. Gronchi and A. Milani, Proper elements for Earth crossing asteroids, Icarus, 152 (2001), 58-69. |
[10] |
G. F. Gronchi and P. Michel, Secular orbital evolution, proper elements and proper frequencies for near-earth asteroids: A comparison between semianalytic theory and numerical integrations, Icarus, 152 (2001), 48-57. |
[11] |
G. F. Gronchi and G. Tommei, On the uncertainty of the minimal distance between two confocal Keplerian orbits, Discrete Contin. Dyn. Syst. Ser. B, 7 (2007), 755-778.
doi: 10.3934/dcdsb.2007.7.755. |
[12] |
K. V. Kholshevnikov and N. Vassiliev, On the distance function between two keplerian elliptic orbits, Cel. Mech. Dyn. Ast., 75 (1999), 75-83.
doi: 10.1023/A:1008312521428. |
[13] |
H. Kinoshita and H. Nakai, General solution of the Kozai mechanism, Cel. Mech. Dyn. Ast., 98 (2007), 67-74.
doi: 10.1007/s10569-007-9069-6. |
[14] |
Y. Kozai, Secular perturbation of asteroids with high inclination and eccentricity, Astron. Journ., 67 (1962), 591-598. |
[15] |
M. L. Lidov, The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies, Plan. Spa. Sci., 9 (1962), 719-759. |
[16] |
A. Milani, S. R. Chesley, M. E. Sansaturio, G. Tommei and G. Valsecchi, Nonlinear impact monitoring: Line of variation searches for impactors, Icarus, 173 (2005), 362-384. |
[17] |
A. Milani and G. F. Gronchi, "Theory of Orbit Determination," Cambridge Univ. Press, 2010. |
[18] |
G. B. Valsecchi, A. Milani, G. F. Gronchi and S. R. Chesley, Resonant returns to close approaches: Analytical theory, Astron. Astrophys., 408 (2003), 1179-1196. |
[19] |
A. Whipple, Lyapunov times of the inner asteroids, Icarus, 115 (1995), 347-353. |
show all references
References:
[1] |
V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, "Mathematical Aspects of Classical and Celestial Mechanics," Springer, 1997. |
[2] |
R. V. Baluyev and K. V. Kholshevnikov, Distance between Two Arbitrary Unperturbed Orbits, Cel. Mech. Dyn. Ast., 91 (2005), 287-300.
doi: 10.1007/s10569-004-3207-1. |
[3] |
E. Bowell and K. Muinonen, Earth-crossing asteroids and comets: Groundbased search strategies, in "Hazards due to Comets & Asteroids" (Ed. T. Gehrels), Tucson: The University of Arizona Press, (1994), 149-197. |
[4] |
R. A. Broucke and P. J. Cefola, On the equinoctial orbit elements, Cel. Mech. Dyn. Ast., 5 (1972), 303-310. |
[5] |
G. F. Gronchi, Generalized averaging principle and the secular evolution of planet crossing orbits, Cel. Mech. Dyn. Ast., 83 (2002), 97-120.
doi: 10.1023/A:1020178613365. |
[6] |
G. F. Gronchi, On the stationary points of the squared distance between two ellipses with a common focus, SIAM Journ. Sci. Comp., 24 (2002), 61-80.
doi: 10.1137/S1064827500374170. |
[7] |
G. F. Gronchi, An algebraic method to compute the critical points of the distance function between two Keplerian orbits, Cel. Mech. Dyn. Ast., 93 (2005), 297-332.
doi: 10.1007/s10569-005-1623-5. |
[8] |
G. F. Gronchi and A. Milani, Averaging on Earth-crossing orbits, Cel. Mech. Dyn. Ast., 71 (1998), 109-136.
doi: 10.1023/A:1008315321603. |
[9] |
G. F. Gronchi and A. Milani, Proper elements for Earth crossing asteroids, Icarus, 152 (2001), 58-69. |
[10] |
G. F. Gronchi and P. Michel, Secular orbital evolution, proper elements and proper frequencies for near-earth asteroids: A comparison between semianalytic theory and numerical integrations, Icarus, 152 (2001), 48-57. |
[11] |
G. F. Gronchi and G. Tommei, On the uncertainty of the minimal distance between two confocal Keplerian orbits, Discrete Contin. Dyn. Syst. Ser. B, 7 (2007), 755-778.
doi: 10.3934/dcdsb.2007.7.755. |
[12] |
K. V. Kholshevnikov and N. Vassiliev, On the distance function between two keplerian elliptic orbits, Cel. Mech. Dyn. Ast., 75 (1999), 75-83.
doi: 10.1023/A:1008312521428. |
[13] |
H. Kinoshita and H. Nakai, General solution of the Kozai mechanism, Cel. Mech. Dyn. Ast., 98 (2007), 67-74.
doi: 10.1007/s10569-007-9069-6. |
[14] |
Y. Kozai, Secular perturbation of asteroids with high inclination and eccentricity, Astron. Journ., 67 (1962), 591-598. |
[15] |
M. L. Lidov, The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies, Plan. Spa. Sci., 9 (1962), 719-759. |
[16] |
A. Milani, S. R. Chesley, M. E. Sansaturio, G. Tommei and G. Valsecchi, Nonlinear impact monitoring: Line of variation searches for impactors, Icarus, 173 (2005), 362-384. |
[17] |
A. Milani and G. F. Gronchi, "Theory of Orbit Determination," Cambridge Univ. Press, 2010. |
[18] |
G. B. Valsecchi, A. Milani, G. F. Gronchi and S. R. Chesley, Resonant returns to close approaches: Analytical theory, Astron. Astrophys., 408 (2003), 1179-1196. |
[19] |
A. Whipple, Lyapunov times of the inner asteroids, Icarus, 115 (1995), 347-353. |
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