46 citations · 258 across the 32 of their papers we have counts for
5 papers · 1 filter
Two body problem on a sphere in the presence of a uniform magnetic field
Nataliya A. Balabanova, James Montaldi
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is alw…
Attracting and repelling 2-body problems on a family of surfaces of constant curvature
Luis García-Naranjo, James Montaldi
We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric e…
Generalized point vortex dynamics on
James Montaldi, Amna Shaddad
This is the second of two companion papers. We describe a generalization of the point vortex system on surfaces to a Hamiltonian dynamical system consisting of two or three points…
Reduction and relative equilibria for the 2-body problem in spaces of constant curvature
A. V. Borisov, L. C. García-Naranjo, I. S. Mamaev +1
We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show…
Feynman path integrals and Lebesgue-Feynman measures
James Montaldi, Oleg G. Smolyanov
We call a Lebesgue-Feynman measure (LFM) any generalized measure (distribution in the sense of Sobolev and Schwartz) on a locally convex topological vector space E which is transla…