KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK
The symmetry of simple mechanical systems problem has been studied in the framework of Lie theory. Two systems, i.e. harmonic oscillator and inverse pendulum, have been taken as concrete cases of the analysis. The analysis is applied to both systems by involving symmetry Lie group in order to obtain...
| Main Authors: | , |
|---|---|
| Format: | Thesis |
| Published: |
[Yogyakarta] : Universitas Gadjah Mada
2014
|
| Subjects: |
| _version_ | 1797034904166334464 |
|---|---|
| author | , IRMAN SAID PRASTYO , Dr. rer. nat. Muhammad Farchani Rosyid |
| author_facet | , IRMAN SAID PRASTYO , Dr. rer. nat. Muhammad Farchani Rosyid |
| author_sort | , IRMAN SAID PRASTYO |
| collection | UGM |
| description | The symmetry of simple mechanical systems problem has been studied in
the framework of Lie theory. Two systems, i.e. harmonic oscillator and inverse
pendulum, have been taken as concrete cases of the analysis. The analysis is
applied to both systems by involving symmetry Lie group in order to obtain classical
description. By using biinvariant metric, it can be shown that R
2
-manifold
as phase space for both systems is a symplectic manifold that is also the coadjoint
orbit of Heisenberg Lie group. Next, the dynamic of the system is given
in the form of equation of motion through the application of the Hamiltonian
equations. |
| first_indexed | 2024-03-13T23:19:31Z |
| format | Thesis |
| id | oai:generic.eprints.org:128066 |
| institution | Universiti Gadjah Mada |
| last_indexed | 2024-03-13T23:19:31Z |
| publishDate | 2014 |
| publisher | [Yogyakarta] : Universitas Gadjah Mada |
| record_format | dspace |
| spelling | oai:generic.eprints.org:1280662016-03-04T07:57:30Z https://repository.ugm.ac.id/128066/ KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK , IRMAN SAID PRASTYO , Dr. rer. nat. Muhammad Farchani Rosyid ETD The symmetry of simple mechanical systems problem has been studied in the framework of Lie theory. Two systems, i.e. harmonic oscillator and inverse pendulum, have been taken as concrete cases of the analysis. The analysis is applied to both systems by involving symmetry Lie group in order to obtain classical description. By using biinvariant metric, it can be shown that R 2 -manifold as phase space for both systems is a symplectic manifold that is also the coadjoint orbit of Heisenberg Lie group. Next, the dynamic of the system is given in the form of equation of motion through the application of the Hamiltonian equations. [Yogyakarta] : Universitas Gadjah Mada 2014 Thesis NonPeerReviewed , IRMAN SAID PRASTYO and , Dr. rer. nat. Muhammad Farchani Rosyid (2014) KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK. UNSPECIFIED thesis, UNSPECIFIED. http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=68394 |
| spellingShingle | ETD , IRMAN SAID PRASTYO , Dr. rer. nat. Muhammad Farchani Rosyid KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title | KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title_full | KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title_fullStr | KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title_full_unstemmed | KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title_short | KAJIAN TEORI LIE PADA OSILATOR HARMONIS DAN BANDUL TERBALIK |
| title_sort | kajian teori lie pada osilator harmonis dan bandul terbalik |
| topic | ETD |
| work_keys_str_mv | AT irmansaidprastyo kajianteoriliepadaosilatorharmonisdanbandulterbalik AT drrernatmuhammadfarchanirosyid kajianteoriliepadaosilatorharmonisdanbandulterbalik |