Office: **Room 3066 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), total positivity, 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 Journal of Nonlinear Science as well several Springer Applied Math Book series. 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: **

shortvita.

** Here a long curriculum vita with list of publications:**

vita

**
My book, Nonholonomic Mechanics and Control, is now available from Springer Verlag.
See Springer Verlag
**

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):**

profile

**A link to an interview with Harry Dankowicz at Applied Mechanics
Reviews:**

interview

**A link to the workshop "Control of Nonlinear Physical Systems"
(Blochfest):**

Workshop

**A photo and video album from the fest
:**

Album

**Selected recent files for download here (many more listed in vita):**

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), *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
Suslov problem

(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
Systems

(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
mechanical systems

(with D. Shi, Y. Berchenko-Kogan and D. Zenkov
*in J. Nonlinear Science 27, (2017) 241-283
*

The geometric nature of the Flaschka
Transformation

(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 Systems

(with P. Rooney and C. Rangan
*in IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 63, NO. 3, 2018
*

An extension to the theory of controlled Lagrangians using the Helmholtz conditions

(with with M. Farre)
*in The Journal of Nonlinear Science {\bf 29} (2019), 345-376.
*

Continuous Direct Sparse Visual Odemetry fomr RGB-D Images

(with M. Ghaffari, W. Clark, R. Eustice and J. Grizzle)
*in Proceedings of 2019 Robotics, Science and Systems
*

A Poincare-Bendixon Theorem for Hybrid Systems

(with with W. Clark and L. Colombo)
*in Mathematical Control and Related Fields {\bf 10}, 27-24, 2020.
*

Energy opimization in extrasolar planetary systems: the transistion from
peas-in-pod to runaway growth

(with F. Adams, K.Batygin and G. Laughlin)
*in Monthly Notices of Royal Astronomical Society, Feb. 2020.
*

**
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**

**Other Photos**