Differential invariants of feedback transformations for quasi-harmonic oscillation equations
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 65-72 |
| Journal / Publication | Journal of Geometry and Physics |
| Volume | 113 |
| Online published | 5 Sep 2016 |
| Publication status | Published - Mar 2017 |
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Abstract
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie pseudo-group of local feedback transformations. In particular, considered class describes behavior of conservative mechanical systems. We construct the class of rational differential invariants that separate regular orbits. It is well known that differential invariants form algebra with respect to the operation of addition and multiplication (Alekseevskij et al. 1991). In our case, constructed rational differential operators form a field (in algebraic sense). Rational differential invariants were studied by Rosenlicht (1956, 1963), Kruglikov and Lychagin (2011).
Research Area(s)
- Quasi-harmonic oscillation equations, Feedback transformations, Jet spaces, Infinitesimal transformations, Lie pseudo-groups, Differential invariants
Citation Format(s)
Differential invariants of feedback transformations for quasi-harmonic oscillation equations. / Gritsenko, Dmitry S.; Kiriukhin, Oleg M.
In: Journal of Geometry and Physics, Vol. 113, 03.2017, p. 65-72.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
