Invariant manifolds in mechanics. I: The general construction of coarse theories from fine theories

A general procedure for deriving coarse theories from fine theories is based on the premise that once a choice has been made for a coarse descriptor, a theory for this new descriptor may be viewed as a study of a small but select class of solutions of the equations of the fine theory. Examples in wh...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 1984-12, Vol.84 (4), p.353-373
Main Authors: MUNCASTER, R. G, ANTMAN, S
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
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Summary:A general procedure for deriving coarse theories from fine theories is based on the premise that once a choice has been made for a coarse descriptor, a theory for this new descriptor may be viewed as a study of a small but select class of solutions of the equations of the fine theory. Examples in which the mapping 'pi' from fine states to coarse states is displayed explicitly include the kinetic theory of gases where the basic descriptor is the molecular density function, and the case where finite elasticity is regarded as the fine theory and mass point mechanics the coarse theory. The effect that an invariance group for the fine theory has on invariance groups for the coarse theories to which it gives rise is considered for the theory of finite elasticity and for theories of elastic rods and shells. A critical discussion of the present derivation scheme, the Method of Invariant Manifolds, is also presented.
ISSN:0003-9527
1432-0673
DOI:10.1007/BF00250587