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A coupled nonlinear relative-rotation system is studied, and the Hopf bifurcation is analyzed under the condition of primary resonance and 1:1 internal resonance. In order to control the Hopf bifurcation point, the stability and amplitude of limit cycle, a nonlinear feedback controller is proposed, and numerical calculation can confirm the validity of the method.
[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Inter. J. Theor. Phys. 25 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16 154(in Chinese) [罗绍凯1996北京理工大学学报16 154]
[4] Luo S K 1996 Appl. Math. Mech. 17 683
[5] Luo S K 1998 Appl. Math. Mech. 19 45
[6] Luo S K 2002 Acta Phys. Sin. 51 712(in Chinese)[罗绍凯 2002 物理学报 51 712]
[7] Luo S K 2002 Acta Phys. Sin. 51 1416(in Chinese) [罗绍凯 2002 物理学报 51 1416]
[8] Jia L Q 2003 Acta Phys. Sin. 52 1043(in Chinese)[贾利群 2003 物理学报 52 1043]
[9] Fu J L, Chen X W, Luo S K 1999 Appl. Math. Mech. 21 549
[10] Luo S K 2002 Chin. Phys. Lett. 19 449
[11] Luo S K 2003 Appl. Math. Mech. 24 468
[12] Luo S K, Jia L Q, Cai J L 2003 Chin. Phys. 12 841
[13] Luo S K, Guo Y X, Mei F X 2004 Acta Phys. Sin. 53 2413(in Chinese)[罗绍凯、郭永新、梅凤翔 2004 物理学报 53 2413]
[14] Luo S K, Guo Y X, Mei F X 2004 Acta Phys. Sin. 53 1270(in Chinese)[罗绍凯、郭永新、梅凤翔 2004 物理学报 53 1270]
[15] Luo S K, Cai J L, Jia L Q 2005 Chin. Phys. 14 656
[16] Fu J L, Chen L Q 2006 J. Phys. A 358 5
[17] Jia L Q, Luo S K Zhang Y Y 2007 Acta Phys. Sin. 56 6188(in Chinese)[贾利群、罗绍凯、张耀宇 2007 物理学报 56 6188]
[18] Luo S K 2007 Acta Phys. Sin. 56 5580(in Chinese)[罗绍凯 2007 物理学报 56 5580]
[19] Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys. Sin. 57 2006(in Chinese)[贾利群、罗绍凯、张耀宇 2008 物理学报 57 2006]
[20] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16(in Chinese)[贾利群、崔金超、张耀宇、罗绍凯2009 物理学报 58 16]
[21] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191(in Chinese)[董全林、刘 彬 2002 物理学报 51 2191]
[22] Dong Q L, Wang K, Zhang C X, Liu B 2004 Acta Phys. Sin. 53 337(in Chinese)[董全林、王 坤、张春熹、刘 彬 2004 物理学报 53 337]
[23] 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 物理学报 55 3852]
[24] Zhao W, Liu B 2005 Acta Phys. Sin. 54 4543(in Chinese)[赵 武、刘 彬 2005 物理学报 54 4543]
[25] Meng Z, Liu B 2007 Acta Phys. Sin. 56 6194(in Chinese) [孟 宗、刘 彬 2007 物理学报 56 6194]
[26] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678(in Chinese) [时培明、刘 彬 2007 物理学报 56 3678]
[27] Shi P M, Liu B, Liu S 2008 Acta Phys. Sin. 57 4675(in Chinese) [时培明、刘 彬、刘 爽 2008 物理学报 57 4675]
[28] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329(in Chinese) [孟 宗、刘 彬 2008 物理学报 57 1329]
[29] Shi P M, Liu B, Jiang J S 2009 Acta Phys. Sin. 58 2147(in Chinese) [时培明、刘 彬、蒋金水 2009 物理学报 58 1321]
[30] Liu S, Liu B, Shi P M 2009 Acta Phys. Sin. 58 4383(in Chinese) [刘 爽、刘 彬、时培明 2009 物理学报 58 4383]
[31] Tang J S, Xiao H 2007 Acta Phys. Sin. 56 101(in Chinese) [唐驾时、萧寒 2007 物理学报 56 101]
[32] Zhang W Y, Huseyin K, Ye M 1998 J. Sound Vib. 255 741
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[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Inter. J. Theor. Phys. 25 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16 154(in Chinese) [罗绍凯1996北京理工大学学报16 154]
[4] Luo S K 1996 Appl. Math. Mech. 17 683
[5] Luo S K 1998 Appl. Math. Mech. 19 45
[6] Luo S K 2002 Acta Phys. Sin. 51 712(in Chinese)[罗绍凯 2002 物理学报 51 712]
[7] Luo S K 2002 Acta Phys. Sin. 51 1416(in Chinese) [罗绍凯 2002 物理学报 51 1416]
[8] Jia L Q 2003 Acta Phys. Sin. 52 1043(in Chinese)[贾利群 2003 物理学报 52 1043]
[9] Fu J L, Chen X W, Luo S K 1999 Appl. Math. Mech. 21 549
[10] Luo S K 2002 Chin. Phys. Lett. 19 449
[11] Luo S K 2003 Appl. Math. Mech. 24 468
[12] Luo S K, Jia L Q, Cai J L 2003 Chin. Phys. 12 841
[13] Luo S K, Guo Y X, Mei F X 2004 Acta Phys. Sin. 53 2413(in Chinese)[罗绍凯、郭永新、梅凤翔 2004 物理学报 53 2413]
[14] Luo S K, Guo Y X, Mei F X 2004 Acta Phys. Sin. 53 1270(in Chinese)[罗绍凯、郭永新、梅凤翔 2004 物理学报 53 1270]
[15] Luo S K, Cai J L, Jia L Q 2005 Chin. Phys. 14 656
[16] Fu J L, Chen L Q 2006 J. Phys. A 358 5
[17] Jia L Q, Luo S K Zhang Y Y 2007 Acta Phys. Sin. 56 6188(in Chinese)[贾利群、罗绍凯、张耀宇 2007 物理学报 56 6188]
[18] Luo S K 2007 Acta Phys. Sin. 56 5580(in Chinese)[罗绍凯 2007 物理学报 56 5580]
[19] Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys. Sin. 57 2006(in Chinese)[贾利群、罗绍凯、张耀宇 2008 物理学报 57 2006]
[20] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16(in Chinese)[贾利群、崔金超、张耀宇、罗绍凯2009 物理学报 58 16]
[21] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191(in Chinese)[董全林、刘 彬 2002 物理学报 51 2191]
[22] Dong Q L, Wang K, Zhang C X, Liu B 2004 Acta Phys. Sin. 53 337(in Chinese)[董全林、王 坤、张春熹、刘 彬 2004 物理学报 53 337]
[23] 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 物理学报 55 3852]
[24] Zhao W, Liu B 2005 Acta Phys. Sin. 54 4543(in Chinese)[赵 武、刘 彬 2005 物理学报 54 4543]
[25] Meng Z, Liu B 2007 Acta Phys. Sin. 56 6194(in Chinese) [孟 宗、刘 彬 2007 物理学报 56 6194]
[26] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678(in Chinese) [时培明、刘 彬 2007 物理学报 56 3678]
[27] Shi P M, Liu B, Liu S 2008 Acta Phys. Sin. 57 4675(in Chinese) [时培明、刘 彬、刘 爽 2008 物理学报 57 4675]
[28] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329(in Chinese) [孟 宗、刘 彬 2008 物理学报 57 1329]
[29] Shi P M, Liu B, Jiang J S 2009 Acta Phys. Sin. 58 2147(in Chinese) [时培明、刘 彬、蒋金水 2009 物理学报 58 1321]
[30] Liu S, Liu B, Shi P M 2009 Acta Phys. Sin. 58 4383(in Chinese) [刘 爽、刘 彬、时培明 2009 物理学报 58 4383]
[31] Tang J S, Xiao H 2007 Acta Phys. Sin. 56 101(in Chinese) [唐驾时、萧寒 2007 物理学报 56 101]
[32] Zhang W Y, Huseyin K, Ye M 1998 J. Sound Vib. 255 741
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