Geodesic
An application of the plane curve's standard basis to a certain class of problems from classical mechanics
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 537-543

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It is shown that the moving basis of a curve in polar coordinates can always be considered as a right-handed reference frame moving with acceleration. A system of differential equations is obtained that describes the trajectory of a freely falling body in a non-inertial reference frame coinciding with the standard basis of the curve. Finally, they were solved numerically using the Archimedean spiral, the three-petal rose and the cardioid as examples.
Keywords: relative motion, line curvature, mechanics of curvilinear motion, computer simulation. 
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Sophie B. Bogdanova; Sergey O. Gladkov. An application of the plane curve's standard basis to a certain class of problems from classical mechanics. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 537-543. http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a12/