Anthony Bloch

Office: Room 4842 East Hall.

Office Phone: (734) 6474980

Title: Alexander Ziwet Collegiate Professor 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 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

Here is my research profile (mainly for departmental use):

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

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

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 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 (2016)

The geometric nature of the Flaschka Transformation Systems
(with F. Gay-Balmaz and T.S. Ratiu), in Comm. Math, Phys. 353, 457-517 (2017)

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

Other Photos