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Preface
Author(s) -
Yongxing Jin,
Xiong Hu,
Qinyou Hu,
Tianhao Tang,
Huafeng Wu
Publication year - 1995
Publication title -
journal of inherited metabolic disease
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.462
H-Index - 102
eISSN - 1573-2665
pISSN - 0141-8955
DOI - 10.1007/bf00711366
Subject(s) - citation , computer science , information retrieval , library science
Stochastic geometric mechanics is a new area of research in mathematics and physics, which aims at extending geometric mechanics of classical (deterministic) dynamical systems to the case of systems for which random phenomena must be taken into account. The study of classical dynamical systems with the help of geometrical methods has a long tradition, it suffices perhaps to mention the variational principles (Euler and Lagrange, D’Alembert and Maupertuis...) which were required for their mathematical study, a combination of analytic and geometric methods. Since the work of Lie, ideas and methods coming from the theory of (Lie) groups and differential geometry have played a crucial role in the development of the general theory of dynamical systems. Geometric mechanics incorporates these developments in a unified way, systematically exploiting the intrinsic symmetries of dynamical systems. It successfully describes a large class of natural phenomena, including mechanical systems of rigid bodies and multiparticle systems, as well as continuum systems such as fluids or the continua that are objects of study in acoustic and electromagnetism. However, several phenomena, both in the sciences of nature and society call for an extension of this description in order to cope with phenomena where random influences, e.g., due to uncertainties in the coefficients entering the equations or in external forces, play an important role. This is particularly the case when the systems are large and of high complexity. The efforts to extend geometric mechanics to cope with such random influences have led to the new research area which we precisely call stochastic geometric mechanics. The creation of this new research area was greatly stimulated by a research semester run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne, with the title, “Geometric mechanics-variational and stochastic methods.” The research semester gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to geometry, representation theory, dynamical systems theory) and also areas of physics, control theory, robotics, and life sciences, with