Abstract
For the double pendulum considered in Sect. 2.1.1, starting from a configuration \(q \in \mathcal{Q}\), we consider a small perturbation to arrive at another, neighbouring, configuration, always moving over the surface of the cylinder \(\mathcal{Q}\) (since the system cannot escape the trap of its own configuration space). Intuitively, what we have is a small piece of a curve γ in \(\mathcal{Q}\), which we can identify with a tangent vector v.
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Notes
- 1.
For a more thorough treatment of Newtonian Mechanics in the geometrical setting, see Segev and Ailon (1986).
- 2.
By attaching to each point of γ its tangent vector.
- 3.
The terminology Cosserat medium is often used in the literature to designate the particular case in which the grains can undergo rotations only. For this reason, we use here the longer and more descriptive title. An alternative terminology due to Eringen distinguishes between micropolar and micromorphic media.
- 4.
This idea was introduced mathematically by Cartan and, in a physical context, by the brothers Cosserat.
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Epstein, M. (2014). Physical Illustrations. In: Differential Geometry. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-06920-3_4
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DOI: https://doi.org/10.1007/978-3-319-06920-3_4
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