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Normally stable hamiltonian systems
Computing collinear 4-Body Problem central configurations with given masses
1. | Professor "Eugenio Méndez Docurro 2011", de la Escuela Superior de Física y Matemáticas del IPN, Zacatenco, 07738 México, D F, Mexico |
References:
[1] |
D. G. Saari, "Collisions, Rings, and Other Newtonian N-Body Problems," American Mathematical Society, Providence, Rhode Island, 2005. |
[2] |
F. R. Moulton, The straight line solutions of the problem of N-bodies, Annals of Mathematics, 12 (1910), 1-17.
doi: 10.2307/2007159. |
[3] |
R. Lehmann-Filhés, Ueber swei Fälle des Vielkörpersproblems, Astr. Nachr, 127 (1891), 137-144. |
[4] |
E. Piña, Algorithm for planar Four-Body Problem central configurations with given masses, preprint, arXiv:1006.2430 |
[5] |
E. Piña, New coordinates for the four-body problem, Rev. Mex. Fis., 56 (2010), 195-203. |
[6] |
E. Piña and P. Lonngi, Central configurations for the planar Newtonian four-body problem, Cel. Mech. & Dyn. Astr., 108 (2010), 73-93.
doi: 10.1007/s10569-010-9291-5. |
[7] |
L. Landau and E. Lifshitz, "Mechanics," Pergamon Press, Reading, 1960. |
[8] |
J. L. Lagrange, Solutions analytiques de quelques problèmes sur les piramides triangulaires, Nouv. Mem. Acad. Sci. Berlin, (1773), 149-176. |
[9] |
N. A. Court, Notes on the orthocentric tetrahedra, The American Mathematical Monthly, 41 (1934), 499-523.
doi: 10.2307/2300415. |
[10] |
E. Piña and A. Bengochea, Hyperbolic geometry for the binary collision angles of the three-body problem in the plane, Qualitative Theor. of Dyn. Sys., 8 (2009), 399-417
doi: 10.1007/s12346-010-0009-6. |
[11] |
C. Simó, El conjunto de bifurcación en el problema espacial de tres cuerpos, in "Acta I Asamblea Nacional de Astronomía y Astrofísica," Instituto de Astrofísica. Univ. de la Laguna. Spain, (1975), 211-217. |
[12] |
J. V. Jose and E. J. Saletan, "Classical Mechanics, A Contemporary Approach," Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9780511803772. |
[13] |
A. Bengochea and E. Piña, The dynamics of saturn, janus and epimetheus as a three-body problem in the plane, Rev. Mex. Fis., 55 (2009), 97-105. |
[14] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies," $4^{th}$ edition, Cambridge University Press, Cambridge, 1937. |
[15] |
E. Piña, Rotations with Rodrigues' vector, Eur. J. Phys., 32 (2011), 1171-1178.
doi: 10.1088/0143-0807/32/5/005. |
[16] |
K. R. Meyer, G. R. Hall and D. Offin, "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem," $2^{nd}$ edition, Springer-Verlag, New York, 2009. |
show all references
References:
[1] |
D. G. Saari, "Collisions, Rings, and Other Newtonian N-Body Problems," American Mathematical Society, Providence, Rhode Island, 2005. |
[2] |
F. R. Moulton, The straight line solutions of the problem of N-bodies, Annals of Mathematics, 12 (1910), 1-17.
doi: 10.2307/2007159. |
[3] |
R. Lehmann-Filhés, Ueber swei Fälle des Vielkörpersproblems, Astr. Nachr, 127 (1891), 137-144. |
[4] |
E. Piña, Algorithm for planar Four-Body Problem central configurations with given masses, preprint, arXiv:1006.2430 |
[5] |
E. Piña, New coordinates for the four-body problem, Rev. Mex. Fis., 56 (2010), 195-203. |
[6] |
E. Piña and P. Lonngi, Central configurations for the planar Newtonian four-body problem, Cel. Mech. & Dyn. Astr., 108 (2010), 73-93.
doi: 10.1007/s10569-010-9291-5. |
[7] |
L. Landau and E. Lifshitz, "Mechanics," Pergamon Press, Reading, 1960. |
[8] |
J. L. Lagrange, Solutions analytiques de quelques problèmes sur les piramides triangulaires, Nouv. Mem. Acad. Sci. Berlin, (1773), 149-176. |
[9] |
N. A. Court, Notes on the orthocentric tetrahedra, The American Mathematical Monthly, 41 (1934), 499-523.
doi: 10.2307/2300415. |
[10] |
E. Piña and A. Bengochea, Hyperbolic geometry for the binary collision angles of the three-body problem in the plane, Qualitative Theor. of Dyn. Sys., 8 (2009), 399-417
doi: 10.1007/s12346-010-0009-6. |
[11] |
C. Simó, El conjunto de bifurcación en el problema espacial de tres cuerpos, in "Acta I Asamblea Nacional de Astronomía y Astrofísica," Instituto de Astrofísica. Univ. de la Laguna. Spain, (1975), 211-217. |
[12] |
J. V. Jose and E. J. Saletan, "Classical Mechanics, A Contemporary Approach," Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9780511803772. |
[13] |
A. Bengochea and E. Piña, The dynamics of saturn, janus and epimetheus as a three-body problem in the plane, Rev. Mex. Fis., 55 (2009), 97-105. |
[14] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies," $4^{th}$ edition, Cambridge University Press, Cambridge, 1937. |
[15] |
E. Piña, Rotations with Rodrigues' vector, Eur. J. Phys., 32 (2011), 1171-1178.
doi: 10.1088/0143-0807/32/5/005. |
[16] |
K. R. Meyer, G. R. Hall and D. Offin, "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem," $2^{nd}$ edition, Springer-Verlag, New York, 2009. |
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