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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, (2005).
|
[2] |
F. R. Moulton, The straight line solutions of the problem of N-bodies,, Annals of Mathematics, 12 (1910), 1.
doi: 10.2307/2007159. |
[3] |
R. Lehmann-Filhés, Ueber swei Fälle des Vielkörpersproblems,, Astr. Nachr, 127 (1891), 137. Google Scholar |
[4] |
E. Piña, Algorithm for planar Four-Body Problem central configurations with given masses,, preprint, (). Google Scholar |
[5] |
E. Piña, New coordinates for the four-body problem,, Rev. Mex. Fis., 56 (2010), 195.
|
[6] |
E. Piña and P. Lonngi, Central configurations for the planar Newtonian four-body problem,, Cel. Mech. & Dyn. Astr., 108 (2010), 73.
doi: 10.1007/s10569-010-9291-5. |
[7] |
L. Landau and E. Lifshitz, "Mechanics,", Pergamon Press, (1960).
|
[8] |
J. L. Lagrange, Solutions analytiques de quelques problèmes sur les piramides triangulaires,, Nouv. Mem. Acad. Sci. Berlin, (1773), 149. Google Scholar |
[9] |
N. A. Court, Notes on the orthocentric tetrahedra,, The American Mathematical Monthly, 41 (1934), 499.
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.
doi: 10.1007/s12346-010-0009-6. |
[11] |
C. Simó, El conjunto de bifurcación en el problema espacial de tres cuerpos,, in, (1975), 211. Google Scholar |
[12] |
J. V. Jose and E. J. Saletan, "Classical Mechanics, A Contemporary Approach,", Cambridge University Press, (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. Google Scholar |
[14] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies,", $4^{th}$ edition, (1937).
|
[15] |
E. Piña, Rotations with Rodrigues' vector,, Eur. J. Phys., 32 (2011), 1171.
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, (2009).
|
show all references
References:
[1] |
D. G. Saari, "Collisions, Rings, and Other Newtonian N-Body Problems,", American Mathematical Society, (2005).
|
[2] |
F. R. Moulton, The straight line solutions of the problem of N-bodies,, Annals of Mathematics, 12 (1910), 1.
doi: 10.2307/2007159. |
[3] |
R. Lehmann-Filhés, Ueber swei Fälle des Vielkörpersproblems,, Astr. Nachr, 127 (1891), 137. Google Scholar |
[4] |
E. Piña, Algorithm for planar Four-Body Problem central configurations with given masses,, preprint, (). Google Scholar |
[5] |
E. Piña, New coordinates for the four-body problem,, Rev. Mex. Fis., 56 (2010), 195.
|
[6] |
E. Piña and P. Lonngi, Central configurations for the planar Newtonian four-body problem,, Cel. Mech. & Dyn. Astr., 108 (2010), 73.
doi: 10.1007/s10569-010-9291-5. |
[7] |
L. Landau and E. Lifshitz, "Mechanics,", Pergamon Press, (1960).
|
[8] |
J. L. Lagrange, Solutions analytiques de quelques problèmes sur les piramides triangulaires,, Nouv. Mem. Acad. Sci. Berlin, (1773), 149. Google Scholar |
[9] |
N. A. Court, Notes on the orthocentric tetrahedra,, The American Mathematical Monthly, 41 (1934), 499.
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.
doi: 10.1007/s12346-010-0009-6. |
[11] |
C. Simó, El conjunto de bifurcación en el problema espacial de tres cuerpos,, in, (1975), 211. Google Scholar |
[12] |
J. V. Jose and E. J. Saletan, "Classical Mechanics, A Contemporary Approach,", Cambridge University Press, (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. Google Scholar |
[14] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies,", $4^{th}$ edition, (1937).
|
[15] |
E. Piña, Rotations with Rodrigues' vector,, Eur. J. Phys., 32 (2011), 1171.
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, (2009).
|
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