George Patrick
- Professor
- Applied Mathematics and Mathematical Physics
- Department of Mathematics and Statistics
- University of Saskatchewan
- Saskatoon, SK S7N 5E6
- Canada
- Office: 211 Mclean Hall
- e-mail: patrick@math.usask.ca
- Phone: (306) 966 6084
- FAX: (306) 966 6086
Research Interests
Hamiltonian systems with symmetry, geometric mechanics, numerical simulation.
Publications
- G. W. Patrick,
R. J. Spiteri, W. Zhang and C. Cuell [2009]. On converting any
one-step method to a variational integrator of the same order. 7th
International Conference on Multibody Systems, Nonlinear Dynamics, and
Control, Parts A, B and C 4, 341-349.
- G. W. Patrick and
T. Helmuth [2009]. Two rolling disks or spheres. Discrete
Contin. Dynam. Systems Ser. S 3, 129-140.
- G. W. Patrick and C. Cuell [2009]. Error analysis of variational integrators of unconstrained Lagrangian systems. Numerische Mathematik 113, 243-264. doi:10.1007/s00211-009-0245-3.
- C. Cuell and G. W. Patrick [2009]. Geometric discrete analogues of tangent bundles and constrained Lagrangian systems. J. Geom. Phys. 59, 976-997. doi:10.1016/j.geomphys.2009.04.005.
- C. Cuell and G. W. Patrick [2007]. Skew critical problems. Regul. Chaotic Dyn. 12, 589-601.
- G.W. Patrick, R.M. Roberts, C. Wulff [2008].
Stability Transitions for axisymmetric relative equilibria of Euclidean
symmetric Hamiltonian systems. Nonlinearity 21, 325-352.
- G.W. Patrick [2007]. Variational
development of the semi-symplectic geometry of nonholonomic mechanics.
Rep. Math. Phys. 59, 145-184.
- G.W. Patrick [2006]. Lagrangian
mechanics without ordinary differential equations. Rep. Math.
Phys. 57, 437-443.
- G.W. Patrick [2006]. Variational
proof that relative equilibria are critical points of the amended
potential. Differential Geom. Appl. 24, 479-481.
- G.W.
Patrick, R.M. Roberts, C. Wulff [2004]. Stability of Poisson equilibria
and Hamiltonian relative equilibria by energy methods. Arch. Rational
Mech. Anal. 174, 301-344.
- G.W. Patrick [2003]. Stability
by KAM confinement of certain wild, nongeneric relative equilibria of
underwater vehicles with coincident centers of mass and bouyancy.
SIAM J. Appl. Dyn. Sys. 2, 36-52.
- G.W. Patrick and
R.M. Roberts[2000]. The transversal relative equilibria of a
Hamiltonian system with symmetry. Nonlinearity 13,
2089-2105.
- G.W. Patrick [2001]. The dynamics of
parallel transport. Z. Angew. Math. Mech. (ZAMM) 81,
559-564.
- G.W. Patrick [2000]. Reduction of
the planar 4-vortex system at zero momentum. International conference on
differential equations 2, B. Fiedler, K. Grogerand, and
J. Sprekels Eds., 1000-1008. World Scientific.
- G.W. Patrick [2000]. Dynamics of
perturbed relative equilibria of point vortices on the sphere or plane.
J. Nonlin. Sci. 10, 401-415.
- G.W. Patrick [1999]. The
Landau-Lifshitz equation by semidirect product reduction. Lett. Math.
Phys. 50, 177-188.
- G.W. Patrick [1999]. Dynamics
near relative equilibria: nongeneric momenta at a 1:1 group-reduced
resonance. Math. Z. 232, 747-788.
- J.E. Marsden,
G.W. Patrick, and S. Shkoller [1998]. Multisymplectic geometry,
variational integrators, and nonlinear PDEs. Comm. Math. Phys.
199, 351-395.
- B. Leimkuhler and G.W. Patrick
[1996]. A symplectic integrator for Riemannian manifolds. J. Nonl.
Sci. 6, 367-384.
- G.W. Patrick [1995]. Relative
equilibria of Hamiltonian systems with symmetry: linearization,
smoothness, and drift. Jour. Nonl. Sci. 5, 373-418.
- G.W. Patrick [1992]. Relative
equilibria in Hamiltonian systems: The dynamic interpretation of
nonlinear stability on a reduced phase space. J. Geom. Phys.
9, 111-119.
- G.W. Patrick [1991]. Two axially symmetric
coupled rigid bodies: relative equilibria, stability, bifurcations, and a
momentum preserving symplectic integrator. Doctoral thesis,
University of California at Berkeley, Berkeley, California.
- G.W. Patrick [1985]. Singular momentum mappings, presymplectic dynamics, and gauge groups. Masters thesis,
University of Calgary.
Presentations
-
Variational discretizations: discrete tangent bundles, local error
analysis, and arbitrary order variational integrators
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Towards better understanding the behaviours of rattlebacks
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Towards automatically generated variational integrators
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-
Theory and numerics of stability transitions for falling
spinning underwater vehicles
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Variational recognition for structures of nonholonomic mechanics
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-
Discretizations of Lagrangian Mechanics
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Teaching evaluations
Personal Notes, Favorite Links, etc.
- Department
of Mathematics and Statistics
- College of Arts and Science
- BIRS workshop talks
- BIRS workshop pictures