On the Damped Pinney Equation from Noether Symmetry Principles
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913538518286336 |
|---|---|
| author | Haas, Fernando |
| author_facet | Haas, Fernando |
| contents | There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Damped Pinney Equation from Noether Symmetry Principles Haas, Fernando Classical Physics There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations. |
| title | On the Damped Pinney Equation from Noether Symmetry Principles |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2410.06350 |