The Sitnikov Problem Investigation with the Method of Multiple Scales
Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on it...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Manshadi, Ali Dehghan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Shiraz University 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Iranian journal of science and technology - Cham, Switzerland : Springer International Pubishing, 2004, 42(2017), 3 vom: 13. März, Seite 1471-1477 |
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| Übergeordnetes Werk: |
volume:42 ; year:2017 ; number:3 ; day:13 ; month:03 ; pages:1471-1477 |
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| DOI / URN: |
10.1007/s40995-017-0180-6 |
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SPR038038439 |
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| 520 | |a Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. | ||
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10.1007/s40995-017-0180-6 doi (DE-627)SPR038038439 (SPR)s40995-017-0180-6-e DE-627 ger DE-627 rakwb eng Manshadi, Ali Dehghan verfasserin aut The Sitnikov Problem Investigation with the Method of Multiple Scales 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2017 Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. Sitnikov equation (dpeaa)DE-He213 Perturbation technique (dpeaa)DE-He213 The Method of Multiple Scales (dpeaa)DE-He213 Manshadi, Mojtaba Dehghan aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 42(2017), 3 vom: 13. März, Seite 1471-1477 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:42 year:2017 number:3 day:13 month:03 pages:1471-1477 https://dx.doi.org/10.1007/s40995-017-0180-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 42 2017 3 13 03 1471-1477 |
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10.1007/s40995-017-0180-6 doi (DE-627)SPR038038439 (SPR)s40995-017-0180-6-e DE-627 ger DE-627 rakwb eng Manshadi, Ali Dehghan verfasserin aut The Sitnikov Problem Investigation with the Method of Multiple Scales 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2017 Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. Sitnikov equation (dpeaa)DE-He213 Perturbation technique (dpeaa)DE-He213 The Method of Multiple Scales (dpeaa)DE-He213 Manshadi, Mojtaba Dehghan aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 42(2017), 3 vom: 13. März, Seite 1471-1477 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:42 year:2017 number:3 day:13 month:03 pages:1471-1477 https://dx.doi.org/10.1007/s40995-017-0180-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 42 2017 3 13 03 1471-1477 |
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10.1007/s40995-017-0180-6 doi (DE-627)SPR038038439 (SPR)s40995-017-0180-6-e DE-627 ger DE-627 rakwb eng Manshadi, Ali Dehghan verfasserin aut The Sitnikov Problem Investigation with the Method of Multiple Scales 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2017 Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. Sitnikov equation (dpeaa)DE-He213 Perturbation technique (dpeaa)DE-He213 The Method of Multiple Scales (dpeaa)DE-He213 Manshadi, Mojtaba Dehghan aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 42(2017), 3 vom: 13. März, Seite 1471-1477 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:42 year:2017 number:3 day:13 month:03 pages:1471-1477 https://dx.doi.org/10.1007/s40995-017-0180-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 42 2017 3 13 03 1471-1477 |
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10.1007/s40995-017-0180-6 doi (DE-627)SPR038038439 (SPR)s40995-017-0180-6-e DE-627 ger DE-627 rakwb eng Manshadi, Ali Dehghan verfasserin aut The Sitnikov Problem Investigation with the Method of Multiple Scales 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2017 Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. Sitnikov equation (dpeaa)DE-He213 Perturbation technique (dpeaa)DE-He213 The Method of Multiple Scales (dpeaa)DE-He213 Manshadi, Mojtaba Dehghan aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 42(2017), 3 vom: 13. März, Seite 1471-1477 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:42 year:2017 number:3 day:13 month:03 pages:1471-1477 https://dx.doi.org/10.1007/s40995-017-0180-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 42 2017 3 13 03 1471-1477 |
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10.1007/s40995-017-0180-6 doi (DE-627)SPR038038439 (SPR)s40995-017-0180-6-e DE-627 ger DE-627 rakwb eng Manshadi, Ali Dehghan verfasserin aut The Sitnikov Problem Investigation with the Method of Multiple Scales 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2017 Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. Sitnikov equation (dpeaa)DE-He213 Perturbation technique (dpeaa)DE-He213 The Method of Multiple Scales (dpeaa)DE-He213 Manshadi, Mojtaba Dehghan aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 42(2017), 3 vom: 13. März, Seite 1471-1477 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:42 year:2017 number:3 day:13 month:03 pages:1471-1477 https://dx.doi.org/10.1007/s40995-017-0180-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 42 2017 3 13 03 1471-1477 |
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Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. © Shiraz University 2017 |
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Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. © Shiraz University 2017 |
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Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior. © Shiraz University 2017 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR038038439</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230328194918.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2017 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40995-017-0180-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR038038439</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40995-017-0180-6-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Manshadi, Ali Dehghan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The Sitnikov Problem Investigation with the Method of Multiple Scales</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">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Shiraz University 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate the elliptical form of the Sitnikov equation. Some initial conditions and eccentricities of the primary bodies are studied and results are compared with numerical solution. Results show that estimated analytical solution can help to discover the Sitnikov equation behavior.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sitnikov equation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Perturbation technique</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">The Method of Multiple Scales</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Manshadi, Mojtaba Dehghan</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Iranian journal of science and technology</subfield><subfield code="d">Cham, Switzerland : Springer International Pubishing, 2004</subfield><subfield code="g">42(2017), 3 vom: 13. 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