Office: Room 4842 East Hall.
Office Phone: (734) 6474980
Title: Alexander Ziwet Collegiate Professor of Mathematics and Chair
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 Editor-Chief of the SIAM J. on Control and Optimization. I am a Fellow of the IEEE, a SIAM and AMS Fellow, and have been a Guggenheim Fellow and a Senior Fellow of the Michigan Society of Fellows and a Simons Fellow. Further details in my vita below. I served as Graduate Chair (2002-2005) and Chair (2005-2008) of the Dept. of Mathematics and am currently serving another term as Chair.
Here is a short vita:
Here a long curriculum vita with list of publications:
My book, Nonholonomic Mechanics and Control, is now available from Springer Verlag.
See Springer Verlag
Second edition is is now available at
Nonholonomic Mechanics and Control, Second Edition
My book, The Principal of Least Action, History and Physics, with Alberto Rojo, is available from
Cambridge University Press.
See The Principal of Least Action, Cambridge University Press
Here is my research profile (mainly for departmental use):
A link to an interview with Harry Dankowicz at Applied Mechanics
A link to the workshop "Control of Nonlinear Physical Systems"
A photo and video album from the fest
Selected recent files for download here (many more listed in vita):
Hamiltonian and gradient structures in the
in The Journal of Geometry and Physics, 27 (1998), 230-248 (with M. Gekhtman).
Stablization of nonholonomic systems using isospectral
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
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).
(with J. Marsden and D.Zenkov), Notices 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).
Hill's equation with random forcing terms
(with F. Adams), SIAM. J. Appl. Math 68, 947-980 (2008).
General analysis of type I planetary migration
with stochastic perturbations
(with F. Adams), The Astrophysical Journal 701, 1381-1391 (2009).
Quasivelocities and Symmetries in Nonholonomic Systems
(with J. Marsden and D. Zenkov), Dynamical Systems 24, 187-222 (2009).
A class of integrable flows on the space
of symmetric matrices
(with V. Brinzanescu, A. Iserles, J. Marsden and T. Ratiu), Communications in Mathematical Physics 290, 399-435 (2009).
Hamiltonization of Nonholonomic Systems and
the Inverse Problem of the Calculus of Variations
(with O. Fernandez and T. Mestdag), Reports on Mathematical Physics, 63, 225-249 (2009).
Finite controllability of infinite quantum systems
(with R. Brockett and C. Rangan ), IEEE Transaction Automatic Control, 55, 1897-1205 (2010).
The rolling sphere, the quantum spin and a simple
view of the Landau-Zener problem
(with A. Rojo ), The American Journal of Physics, 78, 1012-1022 (2010).
The Weitzenbock Connection and time
parameterization in nonholonomic mechnaics
(with O. Fernandez ), Journal of Mathematical Physics 52, 012901 (2011)
Embedded geodesic problems and optimal
control for matrix Lie groups
(with P. E. Crouch, N. Nordkvist and A.K. Sanyal), Journal of Geometric Mechanics 3, 197-223 (2011)
Variational inegrators for
Hamiltonizable nonholonomic systems
(with O. Fernandez ), Journal of Geometric Mechanics 4,137-163 (2012)
Mean motion resonances in exoplanet systems:
an investigation into nodding behavior
(with J. Ketchum and F. Adams), Astrophysical Journal, 762, 1-19 (2013)
The evolution of planetary systems with
time-dependent stellar mass loss rates
(with F. Adams and K. Anderson), Monthly Notices of the Royal Astronomical Society, 432, 438 (2013)
The geometry and integrability of the
(with O. Fernandez and D. Zenkov), Journal of Mathematical Physics 55,112704 (2014)
On the stability of extrasolar planets and other
closely orbiting pairs
(with F. Adams), Monthly Notices of the Royal Astronomical Society, 446, 3676-3686 (2015)
A Geometric Approach to the Optimal Control of Nonholonomic Mechanical
(with L. Colombo, R. Gupta and D. Martin), in Analysis and Geometry in Control Theory, Springer INDAM, 35.64 (2015)
A new method for designing stable periodic gaits
(with H. Razavi, C. Chevallereau and J. W. Grizzle) in J. Autonomous Robots doi:10.1007/s10514-016-9593-x, (2016) 1-24 (2016)
Hamel's formalism for Infinite-dimensinal
(with D. Shi, Y. Berchenko-Kogan and D. Zenkov in J. Nonlinear Science 27, (2017) 241-283
The geometric nature of the Flaschka
(with F. Gay-Balmaz and T.S. Ratiu), in Comm. Math, Phys. 353, 457-517 (2017)
Projector-based Control of Orbit Dynamics in
Quantum Lindblad Systemss
(with P. Rooney and C. Rangan in IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 63, NO. 3, 2018
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 AFOSR
Crouch CDC Workshop