6 research outputs found
Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials
In this paper we study the linear stability of the relative equilibria for
homogeneous and quasihomogeneous potentials. Firstly, in the case the potential
is a homogeneous function of degree , we find that any relative equilibrium
of the -body problem with is spectrally unstable. We also find a
similar condition in the quasihomogeneous case. Then we consider the case of
three bodies and we study the stability of the equilateral triangle relative
equilibria. In the case of homogeneous potentials we recover the classical
result obtained by Routh in a simpler way. In the case of quasihomogeneous
potentials we find a generalization of Routh inequality and we show that, for
certain values of the masses, the stability of the relative equilibria depends
on the size of the configuration.Comment: 21 pages 4 figure
On the Global Existence of Bohmian Mechanics
We show that the particle motion in Bohmian mechanics, given by the solution
of an ordinary differential equation, exists globally: For a large class of
potentials the singularities of the velocity field and infinity will not be
reached in finite time for typical initial values. A substantial part of the
analysis is based on the probabilistic significance of the quantum flux. We
elucidate the connection between the conditions necessary for global existence
and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe