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JOURNAL OF GEOMETRIC MECHANICSdoi:10.3934/jgm.2020028c©American Institute of Mathematical SciencesVolume12, Number3, September2020pp.i–ivPREFACE TO THE SPECIAL ISSUE DEDICATEDTO JAMES MONTALDIIn August 2018 we held a conference in Guanajuato, Mexico, where several col-laborators and students of James Montaldi had the privilege to homage his scien-tific contributions. James is best known as an expert in singularity and bifurcationtheory, who is a world reference in equivariant Hamiltonian systems, and has anexceptional talent to turn symmetries into insightful theorems about the dynamicsof mechanical systems. His unusual combination of mathematical depth, modesty,integrity and friendly personality, make him a greatly esteemed member of theextended geometric mechanics community.The programme of this exciting meeting, which lasted one week, incorporatedsome of the many areas in which James has worked over the years. During theconference, we heard testimonials of James’ mathematical sharpness, kindness andgenerosity as a supervisor and collaborator, accompanied with many nostalgic ref-erences of a meeting that he organised in Peyresq twenty years ago. This issue oftheJournal of Geometric Mechanicsis a continuation of our celebration of James’career and of our appreciation of having him as a teacher, colleague and friend.

A Lie groupoid, called material Lie groupoid, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called material algebroid, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of G−structures is discussed in detail. An illustrative example is presented as an application of the theory. © 2019 American Institute of Mathematical Sciences. All rights reserved.

A close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces., Peer Reviewed, Preprint