Remembering Jerry Marsden (1942–2010) Tudor Ratiu and Alan Weinstein, Coordinating Editors Jerrold Eldon Marsden, known to all his friends and other than H. S. M. Coxeter. This was followed by colleagues as Jerry, was born in Ocean Falls, British two papers in 1966 with Mary Beattie and Richard Columbia, on August 17, 1942. He passed away at Sharpe [4], [5], one on finite projective planes home in Pasadena, California, on September 21, and one on a categorical approach to separation 2010. axioms in topology. Already in this earliest work, Looking at the long and wide-ranging list (num- one can see the interest in symmetry which guided bering 367 in MathSciNet as of January 13, 2011) Jerry’s view of mathematics and mechanics. of published books Jerry began his graduate work at Princeton in and articles by Jer- 1965, where his interests in analysis and me- rold E. (or J. E.) chanics were stimulated by contact with Ralph Marsden, someone Abraham, Gustave Choquet, and Arthur Wight- who did not know man (among others). Another result was the Jerry could be beginning of Jerry’s long career in book writ- forgiven for think- ing and editing. He assisted Abraham in the ing that “Marsden” writing of Foundations of Mechanics [1], Choquet was the pseudonym with the three-volume Lectures on Analysis [15], of a collaborative and Wightman with his Princeton Lectures on group consisting of Statistical Mechanics [38]. In 1968 he completed several pure and his Ph.D. thesis under Wightman’s direction on applied mathemati- Photo by George Bergman. cians. (This may have Hamiltonian One Parameter Groups and General- Jerry Marsden, Berkeley, 1997. already been written ized Hamiltonian Mechanics and came to Berkeley about others, such as Halmos or Lang, but it ap- as a Lecturer in Mathematics. He was appointed plies to Jerry as much as to anyone.) In fact, as the as an assistant professor in 1969 and remained testimonials below illustrate in many ways, Jerry, at Berkeley until 1995. From 1988 until he left, he our dear friend and colleague, was a distinctive was also a professor of electrical engineering and individual as well as a great scientist. computer science. Jerry’s first publication, written when he was an Jerry’s thesis was published as two back-to-back undergraduate at the University of Toronto and articles in the Archive of Rational Mechanics and appearing in the Canadian Mathematical Bulletin Analysis [23], [24]. This work on flows “generated” in 1965 [22], was a note concerning products of by nonsmooth Hamiltonians was motivated in part involutions in Desarguesian projective planes. It by problems of Hamiltonian dynamics in infinite was reviewed in Mathematical Reviews by none dimensions, the subject of much of Jerry’s work throughout his life. Rereading this work today, one Tudor Ratiu is chaired professor of geometric analysis in also sees ideas which have reappeared recently in the Department of Mathematics at the École Polytechnique Fédérale de Lausanne and director of the Bernoulli Center. the theory of continuous Hamiltonian dynamics His email address is [email protected]. (see [41]). Alan Weinstein is professor of the Graduate School in the The next decade was marked by the choice of Department of Mathematics at the University of California, many of the subjects to which Jerry would devote Berkeley. His email address is [email protected]. the rest of his life. The first was his major work with DOI: http://dx.doi.org/10.1090/noti852 David Ebin [18], [19], applying infinite-dimensional 758 Notices of the AMS Volume 59, Number 6 geometric analysis to prove uniqueness and short- structures. At the same time, he worked on foun- time existence of solutions to the Euler equations dational problems in mechanics, all related to of motion for ideal, homogeneous, incompressible reduction, from all possible points of view: Hamil- fluids. This paper remains to this day the model tonian, Lagrangian, Dirac. Stabilization problems of global analysis techniques in the study of fluid and control continued to be a major area of re- motion; its methods have been extended to in- search, as well as dynamical systems, geometric compressible inhomogeneous Euler equations, to mechanics, global analysis, elasticity, and fluid the averaged Euler equations, and to the Camassa- mechanics. Jerry never dropped a subject, he only Holm equation in arbitrary dimensions. Around added to his list of interests. As a result, he saw the same time as the work on fluids, Jerry started bridges between very different areas. For example, a ten-year-long collaboration with Arthur Fischer he would apply ideas from relativity to elastic- (and later others) on the Hamiltonian structure of ity, thereby arriving at remarkable foundational Einstein’s evolution equations. For this work he results. Or he would use geometric mechanics received two prizes in the Relativity Essay Contest ideas in numerical algorithms. Control theory and (with Fischer) in 1973 (1st prize) and in 1976 (2nd dynamical systems techniques would find their prize). The second, significantly enlarged to the ex- way into spacecraft mission design, asteroid orbit tent of being encyclopedic, edition of Foundations analysis, or molecular motion. Discrete differ- of Mechanics appeared in 1978 [2]; it set the tone ential geometry or locomotion problems would for what later became a major field of research: be treated using geometric mechanics and Dirac geometric mechanics. The book Hopf Bifurcation structures. and Its Applications [30] started Jerry’s lifelong For his pioneering work, Jerry work in dynamical systems and bifurcation the- won several major prizes, such ory, to which he later added considerations of as the Norbert Wiener Prize, symmetry. Toward the end of this decade, Jerry the John von Neumann Prize, also became interested in elasticity, a subject on the Humboldt Prize, the Max which he would work in the years to come in col- Planck Research Award, and the laboration with Tom Hughes, Juan Simo, Michael Thomas Caughey Award.He was Ortiz, and other engineers. His 1983 book with a member of both the Canadian Hughes [28] was the first to link deep differential and the London Royal Societies geometric ideas to nonlinear elasticity and is still and the American Academy of today the source and inspiration of much work in Arts and Sciences, and he held this area. an honorary degree from the In the 1980s, Jerry added many items to his University of Surrey. Although long list of research subjects. Work with Weinstein Jerry certainly appreciated this on the Hamiltonian formulation of the Maxwell- recognition, his life was en- Vlasov equations of plasma dynamics led to a riched as much by the personal First lecture. long collaboration with Holm, Ratiu, Weinstein, interaction which he had with so and others in which methods of Poisson geome- many colleagues and students, to whose careers try were used to study the stability of motions he made extraordinary contributions. The pieces in all sorts of continuum systems by the so- below show how others’ lives were enriched by called “energy-Casimir method”, due originally to his. V. I. Arnol’d. Other topics included classical field A list of Jerry Marsden’s coauthors may be theory, geometric phases, and control theory (with found at http://ams.rice.edu/mathscinet/ Bloch and others). search/author.html?mrauthid=120260 and a Towards the middle of the 1980s, Jerry became list of his Ph.D. students at http://genealogy. more and more interested in structure-preserving math.ndsu.nodak.edu/id.php?id=28380. algorithms and engineering problems. As his work on control theory began to move to the center of Anthony M. Bloch his attention, his research shifted gradually to- ward engineering mathematics. One result of this In 1986, when I was a postdoc at the University change of focus was his move to the Control and of Michigan, I was fortunate enough to meet Jerry Dynamical Systems Program at Caltech in 1995. at a conference in Boulder. Jerry, who was in During the last fifteen years of his life, Jerry the audience, came up after my talk to introduce added yet more topics to his list of interests, himself. I was surprised and flattered to learn that including nonholonomic mechanics, structure- preserving algorithms, variational calculus for Anthony M. Bloch is Alexander Ziwet Collegiate professor mechanical systems (both continuous and dis- of mathematics at the University of Michigan. His email crete), mission design for spacecraft, and Dirac address is [email protected]. June/July 2012 Notices of the AMS 759 he had read a couple of my papers, one on infinite- systems, and the work of Roger Brockett, Peter dimensional Hamiltonian systems and another on Crouch, and Arjan van der Schaft on Lagrangian coupled flexible and rigid body motion. This was and Hamiltonian control systems (see e.g., [13]). the beginning of a wonderful collaboration and The work of Grizzle and Marcus in turn influenced friendship which has enriched both my academic the work of Jerry and his student Gloria Alvarez and personal life over the past twenty-five years. Sanchez on Poisson control systems. This work, A couple of years later, Jerry invited me to visit together with earlier work of Krishnaprasad, in- him and Phil Holmes at Cornell University. This spired our joint work on controlled Lagrangian turned out to be a great experience for me both systems (see e.g., [11]). This work used the geom- professionally and personally, and I continued to etry of mechanical systems, and specifically the see much of Jerry after that. We met at Berkeley mechanical connection, to construct a controlled and Ohio State and later at Caltech and Michigan, system that remained Lagrangian.