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pro vyhledávání: '"Patrick, G. W."'
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one of the solu
Externí odkaz:
http://arxiv.org/abs/1912.08900
Publikováno v:
Nonlinearity 21 325--352 2008
In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian
Externí odkaz:
http://arxiv.org/abs/0705.1552
Autor:
Cuell, C., Patrick, G. W.
Skew critical problems occur in continuous and discrete nonholonomic Lagrangian systems. They are analogues of constrained optimization problems, where the objective is differentiated in directions given by an apriori distribution, instead of tangent
Externí odkaz:
http://arxiv.org/abs/0704.3756
Autor:
Patrick, G. W.
A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.
Externí odkaz:
http://arxiv.org/abs/math-ph/0510085
Autor:
Patrick, G. W.
The system of four point vortices in the plane has relative equilibria that behave as composite particles, in the case where three of the vortices have strength $-\Gamma/3$ and one of the vortices has strength $\Gamma$. These relative equilibria occu
Externí odkaz:
http://arxiv.org/abs/math-ph/9910012
Autor:
Patrick, G. W.
Stable assemblages of localized vortices exist which have particle-like properties, such as mass, and which can interact with one another when they closely approach. In this article I calculate the mass of these localized states and numerically inves
Externí odkaz:
http://arxiv.org/abs/math/9906112
Autor:
Patrick, G. W.
The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages.
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Externí odkaz:
http://arxiv.org/abs/math/9905085
Autor:
Patrick, G. W.
Publikováno v:
Math. Z. 232 (1999) 747-787
An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some of the sh
Externí odkaz:
http://arxiv.org/abs/math/9904078
Autor:
Patrick, G. W., Roberts, R. M.
We show that, given a certain transversality condition, the set of relative equilibria $\mcl E$ near $p_e\in\mcl E$ of a Hamiltonian system with symmetry is locally Whitney-stratified by the conjugacy classes of the isotropy subgroups (under the prod
Externí odkaz:
http://arxiv.org/abs/math/9902098
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