Abstract
As implied by the paradigm outlined above, generalized forces are modeled mathematically as elements of the dual space \(C^{r}(\pi )^{*}=C^{r}(W)^{*}\) of the space of \(C^{r}\)-sections of a vector bundle \(\pi :W\to \mathcal {X}\). This section reviews the basic notions corresponding to such continuous linear functionals, with particular attention to localization properties. We start with the case where \(\mathscr {X}\) is a manifold without boundary and continue with the case where bodies are modeled by compact manifolds with corners.
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Segev, R. (2023). Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals. In: Foundations of Geometric Continuum Mechanics. Advances in Mechanics and Mathematics(), vol 49. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-35655-1_17
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DOI: https://doi.org/10.1007/978-3-031-35655-1_17
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