Turkish Journal of Mathematics
DOI
10.3906/mat-1902-73
Abstract
In this work we consider the Riemannian geometry associated with the differential equations of one dimensional simple and damped linear harmonic oscillators. We show that the sectional curvatures are completely determined by the oscillation frequency and the friction coefficient and these physical constants can be thought as obstructions for the manifold to be flat. Moreover, equations of simple and damped harmonic oscillators describe nonisomorphic solvable Lie groups with nonpositive scalar curvature.
Keywords
Harmonic oscillator, Riemannian geometry, constant scalar curvature, oscillation frequency, damping force, metric Lie groups
First Page
2540
Last Page
2548
Recommended Citation
BAYRAKDAR, ZAHİDE OK and BAYRAKDAR, TUNA
(2019)
"A geometric description for simple and damped harmonic oscillators,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 37.
https://doi.org/10.3906/mat-1902-73
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/37
