Research Interests:

• My interests are in geometries of linear frame bundles, multisymplectic geometries, and geometric mechanics, with applications in classical mechanics, field theories, and fluid dynamics. For a summary of my research (.pdf) click here.

Research Publications:

• Constant locked inertia tensor trajectories for simple mechanical systems with symmetry, with C. Stoica, J. Geom. Phys. 57 (2007), 1247-1258 (.pdf) (.ps)
• Relative equilibria for the generalized rigid body, with A. Hernández-Garduño and J. E. Marsden, J. Geom. Phys. 53 (2005), 259-274 (revised 2007)    (.pdf   .ps)
• A frame bundle generalization of multisymplectic momentum mappings, Rep. Math. Phys. 53 (2004), 19-37    (.pdf   .ps)
• A frame bundle generalization of multisymplectic geometries, Rep. Math. Phys. 45 (2000), 183-205    (.pdf   .ps )
• Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields, with R. O. Fulp and L. K. Norris, J. Geom. Phys. 20 (1996), 195-206    (.pdf   .ps)
• Generalized symplectic geometry for classical fields and spinors, Diss. Summ. Math. 1 (1996), 235-242    (.pdf   .ps)
• Geometric prequantization on the spin bundle based on n-symplectic geometry: The Dirac equation, with R. O. Fulp and L. K. Norris, Internat. J. Theoret. Phys. 33 (1994), 1011-1028    (.pdf   .ps)

Publications on the Teaching of Mathematics:

• Reforming the mathematics core for engineers and everyone else, Mathematicians and Education Reform Forum Newsletter 16 no. 3 (2004), 6-9    (.pdf)
• Two-part testing, Project Kaleidoscope Roundtable on the Future: Assessment in the Service of Student Learning (Durham, NC) (2002)    (.html)

Research-related links:

• Control and Dynamical Systems at Caltech
• Geometrical Fluid Dynamics and Geometry and Mechanics at the University of Surrey, UK
• Mathematical Physics at North Carolina State University
• arXiv e-print archive at Cornell University