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Soft Solids pp 5–22Cite as

Birkhäuser

Kinematics

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Abstract

Kinematics is the study of motion. This text addresses the kinematics of an idealized material called a continuum, also referred to as a body.

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Notes

  1. 1.

    Lagrangian formulations were studied before Lagrange by Euler, and Eulerian formulations were used before Euler by D’Alembert (private communication with Prof. K.R. Rajagopal, 2011). The incorrect attribution of an idea to one person, which actually belongs to another, pervades our literature and is made rampant by authors propagating these inconsistencies without taking the time to actually read the literature for themselves (Rajagopal 2011b). Throughout this text the author takes exception, from time to time, to commonly held terminologies whenever such inconsistencies, in his mind, seem to exist. This author is by no means a historian, just a person who has a passion for the history of his beloved science, but whose thirst is throttled back by his dyslexia.

  2. 2.

    In the literature, e.g., Sacks (2000) and Freed et al. (2010), γ 1 λ 2 is commonly written as κ 1 and γ 2 λ 1 is written as κ 2. Choosing the description that we did here means that γ 1 and γ 2 retain their physical interpretation of being “magnitudes of shear” that is otherwise lost with the choice of κ 1 and κ 2, which embed λ 2 and λ 1 within them. Mathematically, nothing is wrong with choosing κ 1 and κ 2. It is in their physical interpretation that confusion can arise.

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    Alan D. Freed

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Freed, A.D. (2014). Kinematics. In: Soft Solids. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-03551-2_1

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