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发表于 2025-3-28 16:23:09
Representations in Four-, Three-, Two-Spaced detailed to the cases of four-, three- and two-dimensional manifolds. (The case of one-dimensional manifolds, i.e. curves is not of relevance here, since the curvature tensor, that measures solely the internal geometry of a manifold, degenerates to zero in one dimension.) The above manifolds will
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发表于 2025-3-28 22:33:35
Continuum Kinematics curvilinear coordinates. Expressed in curvilinear coordinates the differential geometry of flat Euclidean space is captured by the Christoffel symbols that take the role of a symmetric and integrable metric connection with associated zero curvature tensor. The position of a physical point together
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发表于 2025-3-29 02:06:10
Elasticityd-order (nonlinear) elasticity. Thereby it shall be noted that both the material and spatial configurations of first- and second-order elasticity ought to be compatible, see Fig. 7.1. Then, two cases may be considered: firstly the material configuration is assumed compatible and the conditions on th