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The symplectic description and transformed condition of canonical transformation are discussed in mechanics. The condition in thermodynamics is proved. The canonical transformation in electromagnetic waveguide is also studied. The conclusion shows that mechanics, thermodynamics and electromagnetic waveguide have a similar structure in symplectic system. It presents a useful attempt to unified theories.
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Keywords:
- thermodynamics /
- electromagnetic waveguide /
- canonical transformation /
- symplectic
[1] Weyl H 1939 The Classical Groups,Their Invariants and Representations (Princeton: Princeton University Press) p1
[2] Feng K, Qin M Z 2003 Symplectic Method in Hamilton System (Hangzhou: Zhejiang Science and Technology Press) p3 (in Chinese) [冯 康、秦孟兆 2003哈密顿系统的辛几何算法(杭州:浙江科学技术出版社)第3页]
[3] Yao W A, Zhong W X 2002 Symplectic Elasticity (Beijing: Higher Education Press) p10 (in Chinese) [姚伟岸、钟万勰 2002 辛弹性力学(北京:高等教育出版社)第10页]
[4] Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian:Dalian University of Technology Press) p39 (in Chinese) [钟万勰 1995 弹性力学求解新体系(大连: 大连理工大学出版社)第39页]
[5] Wu Y, Hu J Y, Yin X G 2002 Adv. Mech. 32 189 (in Chinese) [吴 永、 胡继云、 殷学纲2002力学进展32 189]
[6] Liu S X, Guo Y X, Liu C 2008 Acta Phys. Sin.57 1311 (in Chinese) [刘世兴、 郭永新、 刘 畅 2008 57 1311]
[7] Wen G Y 1999 J. Microwaves 15 68 (in Chinese) [文舸一 1999 微波学报 15 68]
[8] Bogolubov J N N, Prykarpatsky A K, Taneri U, Prykarpatsky Y A 2009 J. Phys. A: Math. Theor. 42 1
[9] Hou G L, Alatancang 2008 Chin. Phys. B 17 2754
[10] Chen J F, Zhu B, Zhong W X 2009 Acta Phys. Sin.58 1091 (in Chinese) [陈杰夫、 朱 宝、钟万勰 2009 58 1091]
[11] Chen J F, Zheng C L, Zhong W X 2006 Acta Phys. Sin.55 2340 (in Chinese) [陈杰夫、 郑长良、 钟万勰2006 55 2340 ]
[12] Zhong W X 2003 Acta Mech. Sin.4 401 (in Chinese)[钟万勰2003力学学报 4 401]
[13] Hai W H 1994 J. Hunan Educational Institute 12 29 (in Chinese) [海文华 1994 湖南教育学院学报 12 29]
[14] Miroslav G, Hans C O 1997 Phys. Rev. 56 6620
[15] Zhou Y B 1986 Theoretical Mechanics (Beijing: Higher Education Press) p327 (in Chinese) [周衍柏 1986 理论力学教程(北京:高等教育出版社)第327页]
[16] Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p31(in Chinese)[钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第31页]
[17] Hou B H 1997 J. Nanjing Univ. (Natl. Sci. Ed.) 33 35(in Chinese) [侯碧辉 1997 南京大学学报 (自然科学版)33 35]
[18] Zhao K H, Luo W Y 1998 Thermology (Beijing: Higher Education Press) p187 (in Chinese) [赵凯华、罗蔚茵 1998 热学(北京:高等教育出版社)第187页] 〖19] Zhong W X 2001 J. Dalian Univ. Tech. 41 379 (in Chinese) [钟万勰2001 大连理工大学学报41 379 ]
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[1] Weyl H 1939 The Classical Groups,Their Invariants and Representations (Princeton: Princeton University Press) p1
[2] Feng K, Qin M Z 2003 Symplectic Method in Hamilton System (Hangzhou: Zhejiang Science and Technology Press) p3 (in Chinese) [冯 康、秦孟兆 2003哈密顿系统的辛几何算法(杭州:浙江科学技术出版社)第3页]
[3] Yao W A, Zhong W X 2002 Symplectic Elasticity (Beijing: Higher Education Press) p10 (in Chinese) [姚伟岸、钟万勰 2002 辛弹性力学(北京:高等教育出版社)第10页]
[4] Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian:Dalian University of Technology Press) p39 (in Chinese) [钟万勰 1995 弹性力学求解新体系(大连: 大连理工大学出版社)第39页]
[5] Wu Y, Hu J Y, Yin X G 2002 Adv. Mech. 32 189 (in Chinese) [吴 永、 胡继云、 殷学纲2002力学进展32 189]
[6] Liu S X, Guo Y X, Liu C 2008 Acta Phys. Sin.57 1311 (in Chinese) [刘世兴、 郭永新、 刘 畅 2008 57 1311]
[7] Wen G Y 1999 J. Microwaves 15 68 (in Chinese) [文舸一 1999 微波学报 15 68]
[8] Bogolubov J N N, Prykarpatsky A K, Taneri U, Prykarpatsky Y A 2009 J. Phys. A: Math. Theor. 42 1
[9] Hou G L, Alatancang 2008 Chin. Phys. B 17 2754
[10] Chen J F, Zhu B, Zhong W X 2009 Acta Phys. Sin.58 1091 (in Chinese) [陈杰夫、 朱 宝、钟万勰 2009 58 1091]
[11] Chen J F, Zheng C L, Zhong W X 2006 Acta Phys. Sin.55 2340 (in Chinese) [陈杰夫、 郑长良、 钟万勰2006 55 2340 ]
[12] Zhong W X 2003 Acta Mech. Sin.4 401 (in Chinese)[钟万勰2003力学学报 4 401]
[13] Hai W H 1994 J. Hunan Educational Institute 12 29 (in Chinese) [海文华 1994 湖南教育学院学报 12 29]
[14] Miroslav G, Hans C O 1997 Phys. Rev. 56 6620
[15] Zhou Y B 1986 Theoretical Mechanics (Beijing: Higher Education Press) p327 (in Chinese) [周衍柏 1986 理论力学教程(北京:高等教育出版社)第327页]
[16] Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p31(in Chinese)[钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第31页]
[17] Hou B H 1997 J. Nanjing Univ. (Natl. Sci. Ed.) 33 35(in Chinese) [侯碧辉 1997 南京大学学报 (自然科学版)33 35]
[18] Zhao K H, Luo W Y 1998 Thermology (Beijing: Higher Education Press) p187 (in Chinese) [赵凯华、罗蔚茵 1998 热学(北京:高等教育出版社)第187页] 〖19] Zhong W X 2001 J. Dalian Univ. Tech. 41 379 (in Chinese) [钟万勰2001 大连理工大学学报41 379 ]
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