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The periodic solution problem of a relative rotation nonlinear system is considered. Firstly, the relative rotation nonlinear dynamic system is established, which contains nonlinear elastic force, commonly damped force and forcing periodic force. Secondly, the result about the nonexistence of periodic solution of the corresponding autonomous system is obtained, and some results about the existence of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The significance is that we generalize the existing results of the literature. Finally an example is given to illustrate that our results are right.
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Keywords:
- relative rotation /
- nonlinear dynamic system /
- periodic solution
[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. Phys. 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 Y Z, Zhou Y Z 2011 Chin. Phys. B 20 040501
[10] Wang K, Guan X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 59 6859]
[11] 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]
[12] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[13] Wang K, Zhu Y L 2010 Neurocomputing 73 3300
[14] Wang K 2011 Nonlinear Analysis: Real World Application 12 1062
[15] Wang X L, Du Z J, Liang J 2010 Nonlinear Analysis: Real World Application 11 4054
[16] Peng S G 2007 Nonlinear Analysis 67 138
[17] Xiao B, Liu B W 2009 Nonlinear Analysis 10 16
[18] Tang Y, Li Y Q 2008 J. Math. Anal. Appl. 340 1380
[19] Gao H, Liu B W 2009 Applied Mathematics and Computation 211 148
[20] Li X J 2007 Chin. Phys. 16 2837
[21] Li X J 2008 Chin. Phys. B 17 1946
[22] Li X J 2010 Chin. Phys. B 19 020202
[23] Li X J 2010 Chin. Phys. B 19 030201
[24] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[25] Zhang J Y, Feng B Y 2000 The Geometric Theory and Bifurcation Problem of Ordinary Differential Equations (Beijing: Peking University Press) (in Chinese) [张锦炎, 冯贝叶 2000 常微分方程几 何理论与分支问题 (北京: 北京大学出版社)]
[26] Li X J 2009 Nonlinear Analysis 71 2764
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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. Phys. 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 Y Z, Zhou Y Z 2011 Chin. Phys. B 20 040501
[10] Wang K, Guan X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 59 6859]
[11] 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]
[12] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[13] Wang K, Zhu Y L 2010 Neurocomputing 73 3300
[14] Wang K 2011 Nonlinear Analysis: Real World Application 12 1062
[15] Wang X L, Du Z J, Liang J 2010 Nonlinear Analysis: Real World Application 11 4054
[16] Peng S G 2007 Nonlinear Analysis 67 138
[17] Xiao B, Liu B W 2009 Nonlinear Analysis 10 16
[18] Tang Y, Li Y Q 2008 J. Math. Anal. Appl. 340 1380
[19] Gao H, Liu B W 2009 Applied Mathematics and Computation 211 148
[20] Li X J 2007 Chin. Phys. 16 2837
[21] Li X J 2008 Chin. Phys. B 17 1946
[22] Li X J 2010 Chin. Phys. B 19 020202
[23] Li X J 2010 Chin. Phys. B 19 030201
[24] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[25] Zhang J Y, Feng B Y 2000 The Geometric Theory and Bifurcation Problem of Ordinary Differential Equations (Beijing: Peking University Press) (in Chinese) [张锦炎, 冯贝叶 2000 常微分方程几 何理论与分支问题 (北京: 北京大学出版社)]
[26] Li X J 2009 Nonlinear Analysis 71 2764
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