Abstract
In this chapter, we first consider force resultants. invariance properties of forces and stresses, and equilibrium by assuming a group action on the space manifold. Then, for a proto-Galilean spacetime model, where spacetime is modeled as a general fiber bundle over the time axis, we develop the equations for the dynamics of a particle and a body, as an application of the theory presented in the previous chapter.
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References
R. Segev and M. Epstein. Some geometrical aspects of continuum mechanics. Technical Report 158, 1980.
R. Segev and M. Epstein. Proto-Galilean dynamics of a particle and a continuous body. Journal of Elasticity, 2022. to appear.
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Segev, R. (2023). Symmetry and Dynamics. 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_13
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DOI: https://doi.org/10.1007/978-3-031-35655-1_13
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-35654-4
Online ISBN: 978-3-031-35655-1
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