
http://www.dynamicalsystems.org/ma/ma/display?item=359
Dynamical Systems Magazine
October, 2010
To the memory of Jerrold E. Marsden
Jerry Marsden, one of the world's preeminent mechanicians and applied mathematicians, died on September 21st, 2010 after a 12year 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 ... NavierStokes 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 10page paper that Jerry and Alan published in Reports on Mathematical Physics.) Their grouptheoretic viewpoint incorporated symmetries, conservation laws, holonomic and nonholonomic 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 sayperhaps with only a slight danger of oversimplificationthat 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, coauthoring 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 finitedimensional techniques of dynamical systems theory to the infinitedimensional 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 nonholonomicallyconstrained 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 saddletype orbits could be used to steer spacecraft through long, fuelefficient 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 cochair 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 midAugust he was still processing papers for the Journal of Nonlinear Science, of which he was EditorinChief 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 welldeserved 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 erraticallyeducated 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. 
