Research

My current research is in Geometric Mechanics, which can perhaps most easily be described as Hamiltonian Mechanics on manifolds, and specifically in Nonholonomic Mechanics.

I am presently researching the Hamiltonian-like properties of some special types of nonholonomic systems, through ideas in symplectic geometry and the theory of integrable systems.

Publications:

[8] Fernandez, O.E., Bloch, A.M., and Olver, P.J. "Variational Integrators for Hamiltonizable Nonholonomic Systems." Submitted to J. Geometric Mechanics.

[7] Ohsawa, T., Fernandez, O.E., Bloch, A.M., and Zenkov, D.V. "Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization," J. Geometry and Physics, 61(8) (2011), 1263-1291. [pdf] [doi]

[6] Fernandez, O.E. and Bloch, A.M. "The Weitzenbock Connection and Time Reparameterization in Nonholonomic Mechanics," J. Math. Physics, 52(1) 012901 (2011). [pdf] [doi]

[5] Fernandez, O.E., Mestdag, T. and Bloch, A.M. "A Generalization of Chaplygin's Reducibility Theorem," Reg. and Chaotic Dyn., 14(6) (2009). [pdf] [doi]

[4] Mestdag, T., Bloch, A.M. and Fernandez, O.E. "Hamiltonization and geometric integration of nonholonomic systems," Proc. of the 8th Nat. Congress on Theor. and Appl. Mechanics, Brussels (Belgium) (2009). [pdf] [doi]

[3] Bloch, A.M., Fernandez, O.E. and Mestdag, T. "Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations," Rep. Math. Phys. 63 (2009), 225-249. [pdf] [doi]

[2] Fernandez, O.E., Bloch, A.M. and Mestdag, T. "The Pontryagin Maximum Principle applied to Nonholonomic Mechanics," Proceedings of the IEEE 47th Conference on Decision and Control (2008), 4306-4311. [pdf] [doi]

[1] Fernandez, O.E. and Bloch, A.M. "Equivalence of the Dynamics of Nonholonomic and Variational Nonholonomic Systems for Certain Initial Data," J. Phys A: Math. Theor. 41 (2008). [pdf] [doi]

Selected Research Talks and Presentations:

[7] "Variational Integrators for Hamiltonizable Nonholonomic Systems," Mathematical Physics Seminar, Univ. of Minnesota, Minneapolis, MN, Apr. 2010 (invited talk).

[6] "Developing Geometric Integrators for Hamiltonizable Nonholonomic Systems," Institute for Mathematics and its Applications, Minneapolis, MN, Mar. 2010 (invited talk).

[5] "Nonholonomic Systems and their Hamiltonization," 4th International Young Researchers Workshop on Geometry, Mechanics and Control, Ghent, Belgium, Jan. 2010 (invited long talk).

[4] "Falling Cats, Spinning Disks and Snakeboarding: A Tour Through the Mathematics of Mechanics," Wellesley College, Wellesley, MA, Dec. 2009 (invited talk).

[3] "Explicitly Solvable Nonholonomic Systems," AMS Sectional Meeting, University Park, PA, Oct. 2009.

[2] "The Pontryagin Maximum Principle Applied to Nonholonomic Mechanics," IEEE 47th Conference on Decision and Control, Cancun, Mexico, Dec. 2008 (invited talk).

[1] "The Equivalence of the Dynamics of Nonholonomic and Variational Nonholonomic Systems for Certain Initial Data," Applied Dynamics and Geometric Mechanics Conference, Oberwolfach, Germany, Jul. 2008.

Thesis:

Fernandez, O.E. "The Hamiltonization of Nonholonomic Systems and its Applications," Ph.D. Thesis, University of Michigan (2009). [pdf]