-
Conserved quantities of the Cosserat elastic rod dynamics are studied according to the general theorems of dynamics. The rod dynamical equation takes the cross section of the rod as its objective of study and is expressed by two independent variables, the arc coordinate of the rod and the time, so the conserved quantities are written in the integral forms and there exist the arc coordinate conservation and the time conservation. The existence conditions and the formulas of conservations of momentum and moment of momentum are derived from the theorem of momentum and the theorem of moment of momentum respectively, which contain two cases of conserved quanties, one is the time and the other is arc coordinate. Also existence conditions and formulas of conservations of energy about time and are coordinate, which contain mechanical energy conservation, are derived from energy equations about the time and arc coordinate of the rod respectively. All of conservative motions of the rod are explained by examples. The conserved quantities in the integral form are of practical significance in both theoretical and numerical analysis for the Cosserat elastic rod dynamics.
-
Keywords:
- conserved quantities /
- Cosserat elastic rod /
- general theorems of dynamics /
- two independent variables
[1] Liu Y Z 2006 Nonlinear Mechanics of Thin Elastic Rod:Theoritical Basis of Mechanical Model of DNA (Beijing: Tsinghua University Press,Springer) p14,32 (in Chinese)[刘延柱 2006 弹性细杆的非线性力学:DNA力学模型的理论基础(北京:清华大学出版社, Springer) 第14,32页)]
[2] Liu Y Z 2003 Mech.Eng. 25(1) 1 (in Chinese) [刘延柱 2003 力学与实践 25(1) 1]
[3] Ou Yang Z C 2003 Phys. 32 728 (in Chinese) [欧阳钟灿 2003 物理 32 728]
[4] Xue Y, Liu Y Z 2009 Acta Phys. Sin. 58 6737(in Chinese)[薛 纭、刘延柱 2009 58 6737 ]
[5] Liu Y Z, Xue Y, Chen L Q 2004 Acta Phys. Sin. 53 2424(in Chinese)[刘延柱、薛 纭、陈立群 2004 53 2424]
[6] Xue Y, Liu Y Z, Chen L Q 2005 Chin. J. Theor. Appl. Mech. 37 485 (in Chinese) [薛 纭、刘延柱、陈立群 2005 力学学报 37 485]
[7] Xue Y,Liu Y Z 2006 Acta Phys. Sin. 55 3845 (in Chinese)[薛 纭、刘延柱 2006 55 3845]
[8] Xue Y,Weng D W 2009 Acta Phys. Sin. 58 34(in Chinese)[薛 纭、翁德玮 2009 58 34]
[9] Yaoming S, Hearst J E 1994 J. Chem. Phys. 101 5186
[10] Xue Y, Liu Y Z, Chen L Q 2004 Chin. Phys. 13 794
[11] Liu Y Z 2009 Chin. Phys. B 18 1
[12] Cao D Q, Tucker R W 2008 International J. Solids and Structure 45 460
[13] Maddocks J H, Dichmann D J 1994 J. Elasticity 34 83
[14] Zhao W J,Weng Y Q, Fu J L 2007 Chin. Phys. Lett. 24 2773
[15] Wei P J 2007 Integral Equation and Its Numerical Caculation (Beijing: Metallurgical Industry Press) p8(in Chinese)[魏培君 2007 积分方程及其数值计算(北京:冶金工业出版社) 第8页]
[16] Xue Y, Weng D W, Chen L Q 2009 Chin. Quart. Mech. 30(1) 119(in Chinese)[薛 纭、翁德玮、陈立群 2009 力学季刊 30(1)116]
[17] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901(in Chinese)[梅凤翔、尚 玫 2000 49 1901]
[18] Zhang Y, Ge W K 2009 Acta Phys. Sin. 58 7447 (in Chinese)[张 毅、葛伟宽 2009 58 7447]
-
[1] Liu Y Z 2006 Nonlinear Mechanics of Thin Elastic Rod:Theoritical Basis of Mechanical Model of DNA (Beijing: Tsinghua University Press,Springer) p14,32 (in Chinese)[刘延柱 2006 弹性细杆的非线性力学:DNA力学模型的理论基础(北京:清华大学出版社, Springer) 第14,32页)]
[2] Liu Y Z 2003 Mech.Eng. 25(1) 1 (in Chinese) [刘延柱 2003 力学与实践 25(1) 1]
[3] Ou Yang Z C 2003 Phys. 32 728 (in Chinese) [欧阳钟灿 2003 物理 32 728]
[4] Xue Y, Liu Y Z 2009 Acta Phys. Sin. 58 6737(in Chinese)[薛 纭、刘延柱 2009 58 6737 ]
[5] Liu Y Z, Xue Y, Chen L Q 2004 Acta Phys. Sin. 53 2424(in Chinese)[刘延柱、薛 纭、陈立群 2004 53 2424]
[6] Xue Y, Liu Y Z, Chen L Q 2005 Chin. J. Theor. Appl. Mech. 37 485 (in Chinese) [薛 纭、刘延柱、陈立群 2005 力学学报 37 485]
[7] Xue Y,Liu Y Z 2006 Acta Phys. Sin. 55 3845 (in Chinese)[薛 纭、刘延柱 2006 55 3845]
[8] Xue Y,Weng D W 2009 Acta Phys. Sin. 58 34(in Chinese)[薛 纭、翁德玮 2009 58 34]
[9] Yaoming S, Hearst J E 1994 J. Chem. Phys. 101 5186
[10] Xue Y, Liu Y Z, Chen L Q 2004 Chin. Phys. 13 794
[11] Liu Y Z 2009 Chin. Phys. B 18 1
[12] Cao D Q, Tucker R W 2008 International J. Solids and Structure 45 460
[13] Maddocks J H, Dichmann D J 1994 J. Elasticity 34 83
[14] Zhao W J,Weng Y Q, Fu J L 2007 Chin. Phys. Lett. 24 2773
[15] Wei P J 2007 Integral Equation and Its Numerical Caculation (Beijing: Metallurgical Industry Press) p8(in Chinese)[魏培君 2007 积分方程及其数值计算(北京:冶金工业出版社) 第8页]
[16] Xue Y, Weng D W, Chen L Q 2009 Chin. Quart. Mech. 30(1) 119(in Chinese)[薛 纭、翁德玮、陈立群 2009 力学季刊 30(1)116]
[17] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901(in Chinese)[梅凤翔、尚 玫 2000 49 1901]
[18] Zhang Y, Ge W K 2009 Acta Phys. Sin. 58 7447 (in Chinese)[张 毅、葛伟宽 2009 58 7447]
Catalog
Metrics
- Abstract views: 9464
- PDF Downloads: 702
- Cited By: 0
下载:
