Archives of the Mathematisches Forschungsinstitut Oberwolfach.
Jerry Marsden at MFO in 2008.
Jerry Marsden, one of the world's pre-eminent mechanicians and applied
mathematicians, died on September 21st, 2010 after a 12-year battle with
cancer. Jerry's interests were unusually broad; his work influenced
physicists, engineers, life scientists and mathematicians across the
spectrum from pure to applied. In addition to his many publications
(over 400 archival and conference papers, and 21 books), he was a
brilliant expositor and teacher, who always willingly took the time to answer
questions. He motivated and encouraged colleagues and students alike
across an astonishing array of disciplines. He will be sorely missed.
Jerrold Eldon Marsden was born in the small papermill company town of
Ocean Falls, British Columbia on August 17th, 1942. His love of
mathematics was sparked in high school (Burnaby South, BC). He took a
BSc at the University of Toronto in 1965, publishing his first
research paper that year, followed by a PhD at Princeton in 1968,
where he worked with the mathematical physicist Arthur Wightman.
While at Princeton Jerry and Ralph Abraham collaborated on the
Foundations of Mechanics (1967), a seminal work in the new
field of geometric mechanics that Jerry later did so much to shape (a
second, much expanded edition appeared in 1978).
Jerry then began his teaching career as a Lecturer in Mathematics at
the University of California, Berkeley, where he remained for 27 years,
with occasional absences for visiting positions, including 18 months
at Cornell and two Humboldt Fellowships in Germany. In 1995 he
moved to Caltech, ultimately becoming the Carl F. Braun Professor of
Engineering, Control and Dynamical Systems, and Applied and
Computational Mathematics, where he also directed the Center for
Integrative Multiscale Modeling and Simulation (CIMMS) from 2001.
It is difficult to select from Jerry's many contributions, but his
1970 paper with David Ebin on the analysis of fluid flows remains a
classic. In 1966 the great Russian mathematician V.I. Arnold (who also
died earlier this year) reformulated the equations of fluid dynamics in
geometric language. Jerry and David Ebin very cleverly employed
solution techniques from ordinary differential equation theory to solve
these equations. Jerry's colleague Stephen Smale has remarked that it
``provided an elegant way of presenting old and new fundamental work
on the ... Navier--Stokes and Euler equations ... and one of the
first important uses of infinite dimensional manifolds.''
In collaboration with his student Tudor Ratiu, Alan Weinstein, and
many others, Jerry went on to develop deep geometrical foundations,
under the general rubric of reduction theory, for a broad range of
problems in classical and continuum mechanics. (This started in 1974
with a 10-page paper that Jerry and Alan published in Reports on
Mathematical Physics.) Their group-theoretic viewpoint incorporated
symmetries, conservation laws, holonomic and non-holonomic constraints
and control algorithms in a natural way. Over the last 35 years it has
yielded a spectacular array of analytical studies and numerical
algorithms for the solution of practical problems, many of them
developed by Jerry, his students, and collaborators. In 1993 Jerry
noted that ``one can say---perhaps with only a slight danger of
oversimplification---that reduction theory synthesizes the work of
Smale, Arnold (and their predecessors of course) into a bundle, with
Smale as the base and Arnold as the fiber.''
Jerry also made significant contributions to relativity theory with
Arthur Fisher and others, as well as in elasticity theory,
co-authoring
Mathematical Foundations of Elasticity (1983)
with his former master's student Tom Hughes. He was an early exponent
of bifurcation theory and did much to extend finite-dimensional
techniques of dynamical systems theory to the infinite-dimensional
phase spaces of partial differential equations. Yet while developing
abstract ideas and methods in geometric mechanics and dynamics, he
he never lost sight of the details and the painstaking calculations
necessary for success in projects such as proving the existence of
chaotic solutions in specific differential equations, computing spacecraft
orbit trajectories with a group at JPL for the 2001 Genesis Discovery
Mission, and collaborating with his colleague Michael Ortiz to simulate
material behavior in the crushing of aluminum cans.
After moving to Caltech, Jerry developed close connections with a
number of new groups interested in the applications of geometry,
mechanics and control theory to problems in science and
engineering. He was a founding member of the Control and Dynamical
Systems program, whose interdisciplinary PhD program provided many of
his recent students.
During this time he did substantial work to build up the theories of nonholonomically-constrained mechanical systems with symmetry and Lagrangian control systems, and he developed the rich and elegant theory of controlled Lagrangians in collaboration with Tony Bloch, Naomi Leonard and others.
He also began his work in variational integrators, which
exploited the underlying geometric structures to produce numerical
integrators capable of preserving important properties such as energy
and momentum.
This work expanded into studies of optimal control problems and led to
the development of DMOC (discrete mechanics and optimal control)
methods, which were used to solve trajectory generation problems for
mechanical systems. Jerry's emphasis on the need for basic theory in
designing computational methods was a key theme in the CIMMS program
that he directed, and his ideas also found their way into programs
with NASA's Jet Propulsion Laboratory, where Jerry also had many
collaborators. His insight that the structure of stable and unstable
manifolds of saddle-type orbits could be used to steer spacecraft
through long, fuel-efficient tours of the solar system reconnected
deep ideas in geometric dynamics with modern celestial mechanics.
Jerry was also a leader in the development of the theory of Lagrangian
coherent structures (LCS), which he applied to modeling ocean
circulation and underwater robotics. Throughout, he continued to teach
courses that inspired students in a variety of disciplines, including
volunteering to teach freshman mathematics several times, most
recently in Spring 2010.
Jerry did much to advance the mathematical sciences in North America
and beyond, especially in his role as founding Director of Canada's
Fields Institute, initially based at the University of Waterloo and
now located at his alma mater in Toronto. He served on the SIAM Board
of Trustees, as a principal editor of Springer's Applied Mathematics
book series, and on the boards of the Journals of Mathematical Physics
and of Geometry and Physics, Proceedings of the Royal Society, the
Canadian Journal of Applied Mathematics, and the SIAM Journal on
Applied Dynamical Systems, among others. He served on numerous
program and lecture committees, and was co-chair of the
Scientific Program Committee for the 2011 International Congress in
Industrial and Applied Mathematics to be held in Vancouver, BC. He
took on, and discharged with admirable efficiency, more than his share
of editorial and reviewing duties: In mid-August he was still
processing papers for the Journal of Nonlinear Science, of which he
was Editor-in-Chief from 2005.
Jerry's work was recognised by major awards including the John von
Neumann and Norbert Wiener Prizes of SIAM and the AMS, and by election
to the Royal Societies of London and Canada, and the American Academy
of Arts and Sciences. But above these well-deserved honors, it is most
fitting at this time to remember Jerry's encouragement and mentorship
of young people. Few realise that a large part of research is actually
teaching: teaching bright but sometimes erratically-educated students
the necessary background and methods, teaching colleagues and
collaborators about new advances, and teaching oneself all the things
that no one else has done. In his multiple textbooks at all levels, in
his conference presentations and in the lecture hall, Jerry was a
master teacher: delivering deep ideas with elegance, polish, and
humor. His textbook
Vector Calculus, written with Tony
Tromba and subsequently translated into
Spanish, Portugese German and Greek, has been in print for 35
years; he was preparing a sixth edition when he died. His
impact was enormous: in over 42 years he advised 48 PhD theses,
7 MSc theses, and mentored almost 40 postdoctoral fellows, and
it is impossible to definitively count the number of fellow
mathematicians, scientists and engineers with whom he collaborated, or
whose careers and lives he touched. He was especially generous to
young visitors (for many of whom he raised the funds to enable their
visits) and with the students of others, and he responded promptly and
attentively to the many who wrote or approached him with questions at
conferences and workshops. He managed to do this without compromising
the depth of his ideas and thoughts.
Jerry leaves his wife Barbara; his two children, Christopher and Alison;
his grandchildren Eliza and Isaac; a sister Judy MacInnes; and former
wives, Sandra Muirhead and Nancy Brown. Alison has followed in her
father's footsteps; she is a specialist in fluid dynamics and a professor
of Mechanical Engineering at UC San Diego. At the time of his death
Jerry was advising four PhD students, two postdoctoral fellows, and
several undergraduates. In August he enthusiastically told his friend
and former colleague Alan Weinstein about an ongoing undergraduate
research project in spacecraft orbit design, and a week before his
death he was talking on skype about a grant proposal with his former
student Melvin Leok. It's difficult to accept that he won't be showing
up again, bursting with new ideas, with his infectious enthusiasm for
weather and clouds, and his love of nature and animals (especially
dogs).
A memorial service is planned for January 2011 at Caltech, followed by
a conference to honor Jerry's work later in the year. Meanwhile,
remembrances and comments from his friends and colleagues are being
assembled at
http://www.cds.caltech.edu/~marsden/remembrances/
Philip Holmes, Princeton, NJ;
Richard Murray, Pasadena, CA.