Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Albouy, Alain"'
Autor:
Albouy, Alain
A classical theorem states that two confocal ellipsoids, each of them endowed with a surface distribution of mass which is called homeoidal, exert the same Newtonian force on an exterior point if they have the same total mass. We extend this theorem
Externí odkaz:
http://arxiv.org/abs/2408.12453
Autor:
Albouy, Alain, Dullin, Holger R.
Publikováno v:
Geometric Mechanics, Vol. 1, No. 1 (2024) 2450003 (7 pages)
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states. Consequently the
Externí odkaz:
http://arxiv.org/abs/2309.14579
Publikováno v:
Arch. Rational Mech. Anal. (2024) 248:12
Moeckel (1990), Moeckel and Sim\'o (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies
Externí odkaz:
http://arxiv.org/abs/2308.12901
Autor:
Albouy, Alain, Ureña, Antonio J.
Publikováno v:
Celestial Mechanics and Dynamical Astronomy (2023) 135:18
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition case" where infinitely many planes of motion are possible, there are at
Externí odkaz:
http://arxiv.org/abs/2302.06013
Autor:
Albouy, Alain, Ureña, Antonio J.
Publikováno v:
Communications in Contemporary Mathematics, 25 (2023) no 2250041
Consider the equation of the linear oscillator $u"+u=h(\theta)$, where the forcing term $h:\mathbb R\to\mathbb R$ is $2\pi$-periodic and positive. We show that the existence of a periodic solution implies the existence of a positive solution. To this
Externí odkaz:
http://arxiv.org/abs/2201.09272
Autor:
Albouy, Alain, Zhao, Lei
Publikováno v:
Regul. Chaot. Dyn. 27, 253-280 (2022)
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of
Externí odkaz:
http://arxiv.org/abs/2201.00808
Autor:
Albouy, Alain, Dullin, Holger R.
Publikováno v:
Journal of Geometric Mechanics (2020)
The classical equations of the Newtonian 3-body problem do not only define the familiar 3-dimensional motions. The dimension of the motion may also be 4, and cannot be higher. We prove that in dimension 4, for three arbitrary positive masses, and for
Externí odkaz:
http://arxiv.org/abs/2002.00649
Autor:
Albouy, Alain, Urena, Antonio J.
Publikováno v:
Eur. Phys. J. Spec. Top. 229 (2020) 1405-1417
We give simple proofs of some simple statements concerning the Lambert problem. We first restate and reprove the known existence and uniqueness results for the Keplerian arc. We also prove in some cases that the elapsed time is a convex function of n
Externí odkaz:
http://arxiv.org/abs/2001.09301
Autor:
Albouy, Alain, Zhao, Lei
Publikováno v:
Philosophical Transactions of the Royal Society A: mathematical, physical and engineering sciences, 377 (2019)
We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to Lambert's theorem
Externí odkaz:
http://arxiv.org/abs/1910.05391
Autor:
Albouy, Alain
Publikováno v:
Celestial Mechanics and Dynamical Astronomy, 131 (2019), 40
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new proofs. The fi
Externí odkaz:
http://arxiv.org/abs/1711.03049