# To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models

@article{Rizzuti2019ToSR, title={To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models}, author={Bruno Rizzuti and G. F. Vasconcelos J'unior and M{\'a}rcio Ant{\^o}nio Resende}, journal={arXiv: Classical Physics}, year={2019} }

The geodesic has a fundamental role in physics and in mathematics: roughly speaking, it represents the curve that minimizes the arc length between two points on a manifold. We analyze a basic but misinterpreted difference between the Lagrangian that gives the arc length of a curve and the one that describes the motion of a free particle in curved space. Although they provide the same formal equations of motion, they are not equivalent. We explore this difference from a geometrical point of view… CONTINUE READING

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