Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group threory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyse the Euler-Poincar�e equations.

Geometry. --- Mechanics. --- Symmetry (Mathematics). --- Mechanics --- Geometry --- Symmetry (Mathematics) --- Applied Mathematics --- Algebra --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Invariance (Mathematics) --- Group theory --- Automorphisms --- Euclid's Elements --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.

Mathematics. --- Dynamical Systems and Ergodic Theory. --- Differential Geometry. --- Math Applications in Computer Science. --- Mathematical Applications in Computer Science. --- Computer science. --- Differentiable dynamical systems. --- Global differential geometry. --- Mathématiques --- Informatique --- Dynamique différentiable --- Géométrie différentielle globale --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mechanics, Analytic. --- Geometry. --- Dynamics. --- Mechanics. --- Marsden, Jerrold E. --- Classical mechanics --- Newtonian mechanics --- Dynamical systems --- Kinetics --- Analytical mechanics --- Marsden, Jerry --- Marsden, J. --- Marsden, J. E. --- Marsden, Dzh. --- Computer science --- Ergodic theory. --- Computer mathematics. --- Differential geometry. --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Dynamics --- Quantum theory --- Euclid's Elements --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Informatics --- Science --- Computer science—Mathematics. --- Computer mathematics --- Electronic data processing --- Differential geometry --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems. --- Geometry, Differential. --- Dynamical Systems.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Geography --- Stochastic analysis. --- Stochastic models. --- Differential equations. --- Dynamics. --- Nonlinear theories. --- Mathematics of Planet Earth. --- Stochastic Analysis. --- Stochastic Modelling. --- Differential Equations. --- Applied Dynamical Systems. --- Mathematics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Théorie quantique des champs. --- Bosons. --- Spin. --- Théories non linéaires. --- Chaos (théorie des systèmes) --- Quantum field theory. --- Nuclear spin. --- Quantum theory. --- Nonlinear theories. --- Chaotic behavior in systems. --- Théorie quantique des champs. --- Théories non linéaires. --- Chaos (théorie des systèmes)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Geography --- Stochastic analysis. --- Stochastic models. --- Differential equations. --- Dynamics. --- Nonlinear theories. --- Mathematics of Planet Earth. --- Stochastic Analysis. --- Stochastic Modelling. --- Differential Equations. --- Applied Dynamical Systems. --- Oceanografia --- Mathematics.