On Finsler Geometry and Applications in Mechanics: Review and New Perspectives
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 on direction as well as position, and a number of connections emerg...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/828475 |
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| _version_ | 1850179246940487680 |
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| author | J. D. Clayton |
| author_facet | J. D. Clayton |
| author_sort | J. D. Clayton |
| collection | DOAJ |
| description | 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 on
direction 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. |
| format | Article |
| id | doaj-art-9ec32f5d834943a2a424df00d34f583d |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9ec32f5d834943a2a424df00d34f583d2025-08-20T02:18:33ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/828475828475On Finsler Geometry and Applications in Mechanics: Review and New PerspectivesJ. D. Clayton0Impact Physics, US ARL, Aberdeen, MD 21005-5066, USAIn 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 on direction 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.http://dx.doi.org/10.1155/2015/828475 |
| spellingShingle | J. D. Clayton On Finsler Geometry and Applications in Mechanics: Review and New Perspectives Advances in Mathematical Physics |
| title | On Finsler Geometry and Applications in Mechanics: Review and New Perspectives |
| title_full | On Finsler Geometry and Applications in Mechanics: Review and New Perspectives |
| title_fullStr | On Finsler Geometry and Applications in Mechanics: Review and New Perspectives |
| title_full_unstemmed | On Finsler Geometry and Applications in Mechanics: Review and New Perspectives |
| title_short | On Finsler Geometry and Applications in Mechanics: Review and New Perspectives |
| title_sort | on finsler geometry and applications in mechanics review and new perspectives |
| url | http://dx.doi.org/10.1155/2015/828475 |
| work_keys_str_mv | AT jdclayton onfinslergeometryandapplicationsinmechanicsreviewandnewperspectives |