Abstract
Mechanics, the science of motion, was basically started by Galileo and his revolutionary empirical approach. The first precise mathematical formulation was laid down by Newton in the Philosophiae Naturalis Principia Mathematica, first published in 1687, which contained, among many other things, an explanation for the elliptical orbits of the planets around the Sun. Newton’s ideas were developed and extended by a number of mathematicians, including Euler, Lagrange, Laplace, Jacobi, Poisson and Hamilton. Celestial mechanics, in particular, reached an exquisite level of precision: the 1846 discovery of planet Neptune, for instance, was triggered by the need to explain a mismatch between the observed orbit of planet Uranus and its theoretical prediction. This chapter uses Riemannian geometry to give a geometric formulation of Newtonian mechanics.
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Godinho, L., Natário, J. (2014). Geometric Mechanics. In: An Introduction to Riemannian Geometry. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-08666-8_5
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DOI: https://doi.org/10.1007/978-3-319-08666-8_5
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