A geometric description for simple and damped harmonic oscillators

In this work we consider the Riemannian geometry associated with the differential equations of onedimensional simple and damped linear harmonic oscillators. We show that the sectional curvatures are completelydetermined by the oscillation frequency and the friction coefficient and these physical constants can be thought asobstructions for the manifold to be flat. Moreover, equations of simple and damped harmonic oscillators describenonisomorphic solvable Lie groups with nonpositive scalar curvature.

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ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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