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A class of relative rotation nonlinear dynamical model with nonlinear damping force and forcing periodic force is investigated. First, a homotopic mapping is constructed, and then the initial approximate solution is determined. Finally, using the homotopic mapping method, the arbitrarily degree approximation for corresponding model is found.
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Keywords:
- relative rotation /
- nonlinear dynamic equation /
- approximate solution
[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] Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张 凯、 冯 俊 2005 54 2985]
[3] Wang K, 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 54 5530]
[4] 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、 将金水 2006 55 3852]
[5] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明、 刘 彬 2007 56 3678]
[6] Shi P M, Liu, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明、 刘 彬、 侯东晓 2008 57 1321]
[7] 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]
[8] de Jager E M Jiang F R 1996 The Theory of Singular Pertubation, (Amsterdamm, North-Holland Publishing Co)
[9] Sagon G 2008 Nonlinearity 21 1183
[10] Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297
[11] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[12] Ramos M 2009 J. Math. Anal. Appl. 352 246
[13] Mo J Q 2009 Adv. Math. 38 227
[14] Mo J Q 2009 Science in China Ser. G 52 1007
[15] Mo J Q, Lin W T 2008 J, Sys. Sci. & Complexity 20 119
[16] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[17] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[18] Mo J Q 2010 Commun. Theor. Phys. 53 440
[19] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、 林万涛 2004 53 996]
[20] Mo J Q Lin Y H, Lin W 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 58 6692]
[21] Mo J Q 2010 Chin. Phys. B 19 010203
[22] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[23] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[24] Mo J Q 2010 Chin. Phys. B 19 010203
[25] He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和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)]
[26] Liao Shijun 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, (New York, CRC Press 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] Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张 凯、 冯 俊 2005 54 2985]
[3] Wang K, 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 54 5530]
[4] 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、 将金水 2006 55 3852]
[5] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明、 刘 彬 2007 56 3678]
[6] Shi P M, Liu, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明、 刘 彬、 侯东晓 2008 57 1321]
[7] 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]
[8] de Jager E M Jiang F R 1996 The Theory of Singular Pertubation, (Amsterdamm, North-Holland Publishing Co)
[9] Sagon G 2008 Nonlinearity 21 1183
[10] Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297
[11] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[12] Ramos M 2009 J. Math. Anal. Appl. 352 246
[13] Mo J Q 2009 Adv. Math. 38 227
[14] Mo J Q 2009 Science in China Ser. G 52 1007
[15] Mo J Q, Lin W T 2008 J, Sys. Sci. & Complexity 20 119
[16] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[17] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[18] Mo J Q 2010 Commun. Theor. Phys. 53 440
[19] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、 林万涛 2004 53 996]
[20] Mo J Q Lin Y H, Lin W 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 58 6692]
[21] Mo J Q 2010 Chin. Phys. B 19 010203
[22] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[23] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[24] Mo J Q 2010 Chin. Phys. B 19 010203
[25] He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和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)]
[26] Liao Shijun 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, (New York, CRC Press Co)
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