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A class of relational relativistic rotation nonlinear disturbed dynamical equations possessing nonlinear damping force and forcing periodic force is investigated. Firstly, by using the variational principle, the generalized variational iteration is constructed. Then the initial approximate solution is determined. Finally, by using the iteration, the approximation to an arbitray degree for corresponding equation is found.
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Keywords:
- relative rotation /
- dynamic equation /
- variational iteration
[1] Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼, 陈立群, 薛纭 2003 52 256]
[2] Wang K 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 54 5530]
[3] Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese) [赵武, 刘 彬, 时培明, 蒋金水 2006 55 3852]
[4] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘 彬 2007 56 3678]
[5] Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘 彬, 侯东晓 2008 57 1321]
[6] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王 坤, 关新平, 乔杰敏 2010 59 3648]
[7] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[8] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[9] Ramos M 2009 J. Math. Anal. Appl. 352 246
[10] Sagon G 2008 Nonlinearity 21 1183
[11] Mo J Q 2009 Sci. China G 52 1007
[12] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[13] Mo J Q 2010 Commun. Theor. Phys. 53 440
[14] Mo J Q 2010 Chin. Phys. B 19 010203
[15] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[16] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese) [石兰芳, 周先春 2010 59 2915]
[17] Shi L F, Mo J Q 2010 Chin. Phys. B 19 050203
[18] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[19] Shi L F, Zhou X C, Mo J Q 2011 Acta Phys. Sin. B 60 110205 (in Chinese) [石兰芳, 周先春, 莫嘉琪 2011 60 110205]
[20] Shi L F, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 120201 (in Chinese) [石兰芳, 欧阳成, 莫嘉琪 2012 61 120201]
[21] Shi L F, Ouyang C, Chen L H, Mo J Q 2012 Acta Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[22] He J H 2002 Aproximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢2002 工程与科学计算中的近似 非线性分析方法 (郑州: 河南科学技术出版社)]
[23] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co.)
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[1] Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼, 陈立群, 薛纭 2003 52 256]
[2] Wang K 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 54 5530]
[3] Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese) [赵武, 刘 彬, 时培明, 蒋金水 2006 55 3852]
[4] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘 彬 2007 56 3678]
[5] Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘 彬, 侯东晓 2008 57 1321]
[6] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王 坤, 关新平, 乔杰敏 2010 59 3648]
[7] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[8] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[9] Ramos M 2009 J. Math. Anal. Appl. 352 246
[10] Sagon G 2008 Nonlinearity 21 1183
[11] Mo J Q 2009 Sci. China G 52 1007
[12] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[13] Mo J Q 2010 Commun. Theor. Phys. 53 440
[14] Mo J Q 2010 Chin. Phys. B 19 010203
[15] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[16] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese) [石兰芳, 周先春 2010 59 2915]
[17] Shi L F, Mo J Q 2010 Chin. Phys. B 19 050203
[18] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[19] Shi L F, Zhou X C, Mo J Q 2011 Acta Phys. Sin. B 60 110205 (in Chinese) [石兰芳, 周先春, 莫嘉琪 2011 60 110205]
[20] Shi L F, Ouyang C, Mo J Q 2012 Acta Phys. Sin. 61 120201 (in Chinese) [石兰芳, 欧阳成, 莫嘉琪 2012 61 120201]
[21] Shi L F, Ouyang C, Chen L H, Mo J Q 2012 Acta Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[22] He J H 2002 Aproximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢2002 工程与科学计算中的近似 非线性分析方法 (郑州: 河南科学技术出版社)]
[23] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co.)
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