Office: Room 4844 East Hall.
Office Phone: (734) 6474980
Title: Alexander Ziwet Collegiate Professor of Mathematics; Chair, Dept.of Mathematics
My reseach interests include : Hamiltonian and Lagrangian mechanics, symplectic geometry, integrable systems (including the Toda lattice, the dispersionless Toda lattice, geodesic flows and rigid body dynamics), stability, nonholonomic systems (the motion of mechanical systems with nonintegrable constraints), the relationship between continuous and discrete flows, nonlinear control and optimal control. I study various other other topics in geometric mechanics and nonlinear dynamics including quantum dynamics and control. I am on the editorial board of a number of leading journals, and am a Fellow of the IEEE and a Guggenheim Fellow. I hold a number of other awards, details in my vita below.
Here is a curriculum vita with list of publications:
vita
My book, Nonholonomic Mechanics and Control, is now available from Springer Verlag.
See Springer Verlag
For ordering instructions see also
Nonholonomic Mechanics and Control
Here is my research profile (mainly for departmental use):
profile
Selected recent files for download here (many more listed in vita):
Double bracket equations and geodesic flows on symmetric spaces
in Communications on Mathematical Physics 187 (1997), 357-373
(with R. Brockett and P. Crouch).
Hamiltonian and gradient structures in the
Toda flows
in The Journal of Geometry and Physics, 27 (1998), 230-248
(with M. Gekhtman).
Stablization of nonholonomic systems using isospectral
flows
in the SIAM Journal of Control 38 (2000), 855-874
(with S. Drakunov and M. Kinyon).
Dynamics of the n-dimensional Suslov problem
in J. of Geometry of Physics 34 (2000), 121-136 (with D. Zenkov)
Asymptotic Hamiltonian dynamics:
the Toda lattice, the three wave interaction, and the nonholonomic
Chaplygin sleigh
in Physica D 141 (2000). 297-315
The Lyapunov-Malkin theorem and stabilization of the
unicycle with rider
(with D. Zenkov and J. Marsden)
in Systems and Control Letters 46, (2002) 293-302.
The symmetric representation of the
rigid body equations and their discretization
(with P. Crouch, J. Marsden and T. Ratiu)
in Nonlinearity 15, (2002) 1309-1341.
Dispersionsless Toda and Toeplitz Operators
(with F. Golse, T. Paul and A. Uribe), Duke Math. Journal 117, 157-196 (2003).
Invariant measures of nonholonomic
flows with internal degrees of freedom
(with D. Zenkov), Nonlinearity 16, 1793-1807 (2003).
Control of squeezed phonon and spin states
in European Journal of Control 10, 469-477 (with A. Rojo), 2004
Radiation induced instability
SIAM J. Applied Math.(2004) 64, 484-524 (with P. Hagerty and M. Weinstein)
On the optimality of double bracket flows
The International Journal of Mathematics and Mathematical
Sciences 62, 3301-3319 (with A.Iserles), (2004).
Gyroscopically stabilized oscillators and heat baths
(with P. Hagerty, A. Rojo and M. Weinstein), Journal of Stat. Physics
115 1073-1100 (2004).
Dynamic coverage optimal control for interferometric imaging spacecraft formations
(with I. Hussein), Proc. 43rd CDC
1962-1967 (2004).
Nonholonomic Dynamics
(with J. Marsden and D.Zenkov), Notice of the AMS
52 324-333 (2005).
Orbits in extended mass distributions: general
results and the spirographic approximation
(with F. Adams), The Astrophysical Journal
629 204-218 (2005).
A Variational Problem on Stiefel Manifolds
(with P. Crouch and A. Sanyal), Nonlinearity
19 1-30 (2006).
Some joint papers with J. Marsden may be found at Jerry Marsden
Some joint papers with N. Leonard may be found at Naomi Leonard
Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research
