Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Montaldi, James"'
Autor:
Montaldi, James
We provide a systematic study of equilibria of contact vector fields and the bifurcations that occur generically in 1-parameter families, and express the conclusions in terms of the Hamiltonian functions that generate the vector fields. Equilibria oc
Externí odkaz:
http://arxiv.org/abs/2310.00764
This is the first of two companion papers, in which we investigate vortex motion on non-orientable two dimensional surfaces. We establish the `Hamiltonian' approach to point vortex motion on non-orientable surfaces through describing the phase space,
Externí odkaz:
http://arxiv.org/abs/2202.06160
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 always circular, and determined by a simple relation between the velocity
Externí odkaz:
http://arxiv.org/abs/2101.07170
Autor:
García-Naranjo, Luis, Montaldi, James
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 equivalence between repelling particles and attracting particles, and r
Externí odkaz:
http://arxiv.org/abs/1906.01070
Autor:
Montaldi, James, Shaddad, Amna
Publikováno v:
J. Geometric Mechanics, 2019, 11 (4) : 575-599
This is the first of two companion papers. The joint aim is to study a generalization to higher dimension of the point vortex systems familiar in 2-D. In this paper we classify the momentum polytopes for the action of the Lie group SU(3) on products
Externí odkaz:
http://arxiv.org/abs/1809.09020
Autor:
Montaldi, James, Shaddad, Amna
Publikováno v:
J. Geometric Mechanics, 2019, 11 (4) : 601-619
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 on complex projective space CP^2 interacting via a Hamiltonian functio
Externí odkaz:
http://arxiv.org/abs/1809.09007
Autor:
Arathoon, Philip, Montaldi, James
We study the adjoint and coadjoint representations of a class of Lie group including the Euclidean group. Despite the fact that these representations are not in general isomorphic, we show that there is a geometrically defined bijection between the s
Externí odkaz:
http://arxiv.org/abs/1804.09463
We consider the the n-dimensional generalisation of the nonholonomic Veselova problem. We derive the reduced equations of motion in terms of the mass tensor of the body and determine some general properties of the dynamics. In particular we give a cl
Externí odkaz:
http://arxiv.org/abs/1804.09090
Autor:
Fontaine, Marine, Montaldi, James
The LS-category of a topological space is a numerical homotopy invariant, introduced originally in a course on the global calculus of variations by Lyusternik and Schnirelmann, to estimate the number of critical points of a smooth function. When the
Externí odkaz:
http://arxiv.org/abs/1712.07096
Autor:
Fontaine, Marine, Montaldi, James
Publikováno v:
Nonlinearity, Volume 32, Number 6, 2019
Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed in a way that the perturbation preserves only some symmetries of the original system. We give a geometric approach to study this phenomenon in the
Externí odkaz:
http://arxiv.org/abs/1712.05943