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Firstly, the relative rotation nonlinear dynamic system is established, which contains time-varying stiffness, commonly damping force and compulsive periodic force. Secondly, some results of the existence and uniqueness of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The significance is that we generalize the results published in the literature. Furthermore, an example is given to illustrate that our results are new.
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Keywords:
- relative rotation nonlinear dynamic system /
- time-varying stiffness /
- periodic solution /
- existence and uniqueness
[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Int. J. Theor. Phys. 15 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]
[4] Luo S K 1998 Appl. Math. Mech. 19 45
[5] Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[6] Luo S K 2002 Chin. Phy. Lett. 19 449
[7] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[8] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[9] Wang K 2005 Acta Phys. Sin. 54 3987 (in Chinese) [王坤 2005 54 3987]
[10] 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]
[11] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘彬 2007 56 3678]
[12] Meng Z, Liu B 2007 Acta Phys. Sin. 56 6194 (in Chinese) [孟宗, 刘彬 2007 56 6194]
[13] 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]
[14] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[15] Li X J 2007 Chin. Phys. 16 2837
[16] Li X J 2008 Chin. Phys. B 17 1946
[17] Li X J 2010 Chin. Phys. B 19 020202
[18] Li X J 2010 Chin. Phys. B 19 030201
[19] Xiaojing Li 2009 Nonlinear Analysis 71 2764
[20] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations, Berlin: Springer
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[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Int. J. Theor. Phys. 15 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]
[4] Luo S K 1998 Appl. Math. Mech. 19 45
[5] Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[6] Luo S K 2002 Chin. Phy. Lett. 19 449
[7] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[8] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[9] Wang K 2005 Acta Phys. Sin. 54 3987 (in Chinese) [王坤 2005 54 3987]
[10] 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]
[11] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘彬 2007 56 3678]
[12] Meng Z, Liu B 2007 Acta Phys. Sin. 56 6194 (in Chinese) [孟宗, 刘彬 2007 56 6194]
[13] 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]
[14] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[15] Li X J 2007 Chin. Phys. 16 2837
[16] Li X J 2008 Chin. Phys. B 17 1946
[17] Li X J 2010 Chin. Phys. B 19 020202
[18] Li X J 2010 Chin. Phys. B 19 030201
[19] Xiaojing Li 2009 Nonlinear Analysis 71 2764
[20] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations, Berlin: Springer
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