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- W1147751410 abstract "Noether’s theorem is a wellknown tool to draw connections between Lie symmetry groups of a Lagrangian and homogenous balance equations of the volume–type of the associated system. Helmholtz’s equation for vortex motion in an ideal fluid, however, is a balance equation of a different type as compared with those occuring in Noether’s theorem: It is of the area–type; it is outside the scope of Noether’s theorem. An alternative symmetry theorem has been established which connects non–Lie symmetries (e.g. some kinds of regauging transformations) with homogenous balance equations of the area–type. Within this scheme Helmholtz’s equation can be derived. More generally, this alternative concept is adequate to proceed towards the dynamics of line–shaped objects like vortex lines and dislocations in crystals. Consequently, dislocation dynamics can also be formulated within this framework: Based on analogies with the wellknown Lagrangian for fluids I propose Lagrangians for solid bodies in different situations, e.g. in elasticity and plasticity based on dislocation dynamics including thermomechanical effects (dissipation)." @default.
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- W1147751410 date "1998-01-01" @default.
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- W1147751410 title "A balance theorem and its applications to a continuum theory of dislocations and plasticity" @default.
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