Symmetry in Geometric Mechanics and Mathematical Physics
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".
Deadline for manuscript submissions: 30 September 2024 | Viewed by 3381
Special Issue Editors
Interests: differential geometry; symplectic geometry; poisson manifolds; cosserat media; nonholonomic mechanics; geometric integrators; optimal control theory
Special Issue Information
Symmetries are present in natural phenomena, especially in physics. Since the celebrated Noether's Theorem that associates with each symmetry a conserved quantity, the study of symmetries and their implications in the equations of mechanics and mathematical physics has been a constantly growing topic. Since the pioneering work of Evariste Galois, the concept of symmetry has been closely linked to that of the group, and in our field, which requires differentiability, to that of the Lie group. One of the major achievements is the so-called Marsden–Weinstein Theorem of symplectic reduction, which allows us to reduce the dynamical system to another phase space with less dimension. The use of Lie groups and their infinitesimal approximations, Lie algebras, is essential. The moment map becomes a bridge connecting dynamical systems to more manageable algebraic versions. Furthermore, the gauge theories or the construction of the standard model itself are based on the properties of Lie groups.
The concept of the group has been extended to that of the groupoid, which has begun to be used both in particle mechanics (to develop new geometric integrators) and continuum mechanics (for the study of uniformity, evolution, growth, and aging). Symmetries are also extremely useful in the fields of engineering (robotics, for example) and in the study of control systems and economics.
The aim of this Special Issue is to address different aspects of the importance of symmetries in all these areas through the inclusion of quality articles by renowned authors.
Prof. Dr. Manuel de León
Prof. Dr. Narciso Román-Roy
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- particle mechanics
- control systems
- continuum mechanics
- Lie groups
- mathematical physics
- Lie algebras
