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On Finsler Geometry and Applications in Mechanics: Review and New Perspectives
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-31
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
In Finsler geometry, each point of a base manifold can be endowed with coordinates describing its position as well as a set of one or more vectors describing directions, for example.
The associated metric tensor may generally depend ondirection as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients.
Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics.
Here, descriptions of finite deformation of continuous media are of primary focus.
After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed.
A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.
American Psychological Association (APA)
Clayton, J.. 2015. On Finsler Geometry and Applications in Mechanics: Review and New Perspectives. Advances in Mathematical Physics،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1053033
Modern Language Association (MLA)
Clayton, J.. On Finsler Geometry and Applications in Mechanics: Review and New Perspectives. Advances in Mathematical Physics No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1053033
American Medical Association (AMA)
Clayton, J.. On Finsler Geometry and Applications in Mechanics: Review and New Perspectives. Advances in Mathematical Physics. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1053033
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1053033