A Numerical, Literal, and Converged Perturbation Algorithm
The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generat...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
William E. Wiesel [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: The journal of the astronautical sciences - Washington, DC : Springer, 1958, 64(2017), 3, Seite 251-266 |
|---|---|
| Übergeordnetes Werk: |
volume:64 ; year:2017 ; number:3 ; pages:251-266 |
| Links: |
|---|
| DOI / URN: |
10.1007/s40295-016-0112-2 |
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OLC1997075946 |
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| 520 | |a The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. | ||
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| 650 | 4 | |a Iterative methods | |
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| 650 | 4 | |a Perturbation methods | |
| 650 | 4 | |a von Ziepel | |
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10.1007/s40295-016-0112-2 doi PQ20171228 (DE-627)OLC1997075946 (DE-599)GBVOLC1997075946 (PRQ)c1072-3c7a834a908506f3b35dfbcebbffc93073f9046ef6c19135877645d45682fb7e0 (KEY)0035181420170000064000300251numericalliteralandconvergedperturbationalgorithm DE-627 ger DE-627 rakwb eng 620 DE-600 William E. Wiesel verfasserin aut A Numerical, Literal, and Converged Perturbation Algorithm 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. KAM theorem Numerical analysis Perturbations Convergence Numerical methods Iterative methods Theorems Perturbation methods von Ziepel Enthalten in The journal of the astronautical sciences Washington, DC : Springer, 1958 64(2017), 3, Seite 251-266 (DE-627)12935905X (DE-600)160505-7 (DE-576)014731371 0021-9142 nnns volume:64 year:2017 number:3 pages:251-266 http://dx.doi.org/10.1007/s40295-016-0112-2 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-AST SSG-OPC-AST GBV_ILN_70 GBV_ILN_2018 AR 64 2017 3 251-266 |
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10.1007/s40295-016-0112-2 doi PQ20171228 (DE-627)OLC1997075946 (DE-599)GBVOLC1997075946 (PRQ)c1072-3c7a834a908506f3b35dfbcebbffc93073f9046ef6c19135877645d45682fb7e0 (KEY)0035181420170000064000300251numericalliteralandconvergedperturbationalgorithm DE-627 ger DE-627 rakwb eng 620 DE-600 William E. Wiesel verfasserin aut A Numerical, Literal, and Converged Perturbation Algorithm 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. KAM theorem Numerical analysis Perturbations Convergence Numerical methods Iterative methods Theorems Perturbation methods von Ziepel Enthalten in The journal of the astronautical sciences Washington, DC : Springer, 1958 64(2017), 3, Seite 251-266 (DE-627)12935905X (DE-600)160505-7 (DE-576)014731371 0021-9142 nnns volume:64 year:2017 number:3 pages:251-266 http://dx.doi.org/10.1007/s40295-016-0112-2 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-AST SSG-OPC-AST GBV_ILN_70 GBV_ILN_2018 AR 64 2017 3 251-266 |
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10.1007/s40295-016-0112-2 doi PQ20171228 (DE-627)OLC1997075946 (DE-599)GBVOLC1997075946 (PRQ)c1072-3c7a834a908506f3b35dfbcebbffc93073f9046ef6c19135877645d45682fb7e0 (KEY)0035181420170000064000300251numericalliteralandconvergedperturbationalgorithm DE-627 ger DE-627 rakwb eng 620 DE-600 William E. Wiesel verfasserin aut A Numerical, Literal, and Converged Perturbation Algorithm 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. KAM theorem Numerical analysis Perturbations Convergence Numerical methods Iterative methods Theorems Perturbation methods von Ziepel Enthalten in The journal of the astronautical sciences Washington, DC : Springer, 1958 64(2017), 3, Seite 251-266 (DE-627)12935905X (DE-600)160505-7 (DE-576)014731371 0021-9142 nnns volume:64 year:2017 number:3 pages:251-266 http://dx.doi.org/10.1007/s40295-016-0112-2 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-AST SSG-OPC-AST GBV_ILN_70 GBV_ILN_2018 AR 64 2017 3 251-266 |
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10.1007/s40295-016-0112-2 doi PQ20171228 (DE-627)OLC1997075946 (DE-599)GBVOLC1997075946 (PRQ)c1072-3c7a834a908506f3b35dfbcebbffc93073f9046ef6c19135877645d45682fb7e0 (KEY)0035181420170000064000300251numericalliteralandconvergedperturbationalgorithm DE-627 ger DE-627 rakwb eng 620 DE-600 William E. Wiesel verfasserin aut A Numerical, Literal, and Converged Perturbation Algorithm 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. KAM theorem Numerical analysis Perturbations Convergence Numerical methods Iterative methods Theorems Perturbation methods von Ziepel Enthalten in The journal of the astronautical sciences Washington, DC : Springer, 1958 64(2017), 3, Seite 251-266 (DE-627)12935905X (DE-600)160505-7 (DE-576)014731371 0021-9142 nnns volume:64 year:2017 number:3 pages:251-266 http://dx.doi.org/10.1007/s40295-016-0112-2 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-AST SSG-OPC-AST GBV_ILN_70 GBV_ILN_2018 AR 64 2017 3 251-266 |
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10.1007/s40295-016-0112-2 doi PQ20171228 (DE-627)OLC1997075946 (DE-599)GBVOLC1997075946 (PRQ)c1072-3c7a834a908506f3b35dfbcebbffc93073f9046ef6c19135877645d45682fb7e0 (KEY)0035181420170000064000300251numericalliteralandconvergedperturbationalgorithm DE-627 ger DE-627 rakwb eng 620 DE-600 William E. Wiesel verfasserin aut A Numerical, Literal, and Converged Perturbation Algorithm 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. KAM theorem Numerical analysis Perturbations Convergence Numerical methods Iterative methods Theorems Perturbation methods von Ziepel Enthalten in The journal of the astronautical sciences Washington, DC : Springer, 1958 64(2017), 3, Seite 251-266 (DE-627)12935905X (DE-600)160505-7 (DE-576)014731371 0021-9142 nnns volume:64 year:2017 number:3 pages:251-266 http://dx.doi.org/10.1007/s40295-016-0112-2 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-AST SSG-OPC-AST GBV_ILN_70 GBV_ILN_2018 AR 64 2017 3 251-266 |
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The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. |
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The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. |
| abstract_unstemmed |
The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory. |
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| title_short |
A Numerical, Literal, and Converged Perturbation Algorithm |
| url |
http://dx.doi.org/10.1007/s40295-016-0112-2 |
| remote_bool |
false |
| ppnlink |
12935905X |
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n |
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false |
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| doi_str |
10.1007/s40295-016-0112-2 |
| up_date |
2024-07-04T02:08:09.840Z |
| _version_ |
1803612470471819264 |
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Wiesel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A Numerical, Literal, and Converged Perturbation Algorithm</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. 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