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## Euler-Lagrange equation for general n-order character functional and unification of quantitative causal principle, principle of relativity and general Newton’s laws

Zhang Xin-You, L. J. Li, Huang Y. C.
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• #### 摘要

本文获得了有各种相互作用的一般n阶特征量泛函，其耦合系数反映了不同特征量泛函之间的耦合强度. 依据定量因果原理，导出了一般n阶特征量泛函的变分原理，获得了一般n阶特征量泛函的Euler-Lagrange方程，它的不同系数可拟合不同的物理现实，如从线性到任意n阶非线性物理系统，使复杂难解的任意n阶非线性物理系统变得具体可解. 并获得了该对称变换下不变的m个的守恒量，以及它们之间的关系和统一描述. 依据定量因果原理导出了相对性原理，证明了绝对加速参考系、牵连参考系和相对参考系的力都有来自加速度和质量变化的贡献. 利用定量因果原理自然导出了广义牛顿第一定律和广义牛顿第二定律，而且还导出了一个新定律，即广义牛顿第三定律，亦即平移不变性系统合力为零定理. 进而将研究结论应用于对银河系的修正引力势、分子势、夸克禁闭势等，且其结果与物理实验一致.

#### Abstract

This paper gives a general n-order character functional, and uses the quantitative causal principle to derive the general variational principle; furthermore the Euler-Lagrange equation and conservative quantities for a general n-order character functional are derived, and the link between the principle of relativity and the quantitative causal principle is revealed. Newton's first, second, and third laws are then derived, but the third laws is also regarded as a new law: it is a theorem that force is zero in translational invariance, and its general physical meaning in classic mechanics is revealed. The results obtained have been successful applied to the galaxy gravitational potential correction, molecular potential, quark confinement potential, etc., and the results are consistent with the physical experiments.

#### 作者及机构信息

###### 1. 北京工业大学理论物理研究所, 北京 100124; 2. Department of Physics, University of Naples, Via Cintia, 80126 Naples, Italy
• 基金项目: 国家自然科学基金（批准号：11275017，11173028）资助的课题.

#### Authors and contacts

###### 1. Institute of Theoretical Physics, Beijing University of Technology, Beijing 100124, China; 2. Department of Physics, University of Naples, Via Cintia, 80126 Naples, Italy
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11275017, 11173028).

#### 参考文献

 [1] Huang Y C Mechanics Research Communications 30 567 [2] Huang Y C, Li X G 2005 Acta Phys. Sin. 54 3473(in Chinese) [黄永畅, 李希国 2005 物理学报 54 3473] [3] Huang Y C, Li X G 2001 J. Nature 23 227(in Chinese) [黄永畅, 李希国 2001 自然杂志 23 227] [4] Yuan F F, Huang Y C 2013 Classical and Quantum Gravity 30 195008 [5] Ding G T 2009 Acta Phys. Sin. 58 3620(in Chinese) [丁光涛 2009 物理学报 58 3620] [6] Huang Y C, Huang C 2010 International Journal of Theoretical Physics 49 2320 [7] Huang Y C, Lee X G, Shao M X 2006 Modern Physics Letters A 21 1107 [8] Huang C, Huang Y C 2011 Physics Letters A 375 271 [9] Huang Y C, Liao L, Lee X G 2009 The European Physical Journal C 60 481 [10] Moore E N 1983 Theoretical Mechanics (New York: Wiley) [11] Fetter A L, Walecka J D 1980 Theoretical Mechanics of Particles and Continua (New York: McGraw-Hill, International series in pure and applied physics) [12] Mei F X 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1991高等分析力学(北京: 北京理工大学出版社)] [13] Chetaev N G 1989 Theoretical Mechanics (Moscow: Mir Publishers) [14] Georgi H, Glashow S L 1974 Physical Review Letters 32 438 [15] Chen B 1987 Analytical Dynamics (Beijing: Peking University Press ) (in Chinese) [陈斌1987分析动力学(北京: 北京大学出版社)] [16] Wu D J 2013 Modern cosmology (Beijing: Tsinghua University Press) (in Chinese) [吴大江2013现代宇宙学(北京: 清华大学出版社)] [17] Nash C, Sen S 1983 Topology and Geometry for Physicists (London: Academic Press) [18] Pars L A 1965 A Treatise on Analytical Dynamics (London: Heinemann) [19] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York & London: Plenum) [20] Huang Y C, Jiang Y G, Lee X G 2007 Science in China G 50 339 [21] Zou P C, Huang Y C 2012 Physics Letters A 376 3575 [22] Peng Q H 1979 Chinese Science 3 274 [23] Tong Y 1981 Astronomical Journal 22 285 [24] Zheng X T, Tong Y 1984 Astronomical Journal 25 285 [25] Liao L, Huang Y C 2007 Physical Review D 75 025025 [26] Eichten E, Gottfried K, Kinoshita T, Lane K D, Yan T M 1980 Phys. Rev. D 21 203 [27] Liao L, Huang Y C 2007 Annals of Physics 322 2469 [28] Huang Y C, Yu C X 2007 Physical Review D 75 044011 [29] Yu C X, Huang Y C 2007 Physics Letters B 647 49 [30] Zhu Z, Yu H R 1997 Molecular structure and molecular potential energy function (Beijing: Science Press) [31] Huang Y C, Huo Q H 2008 Physics Letters B 662 290 [32] Huang Y C, Yang J L 2008 Physics Letters B 668 438 [33] Huang Y C, Yi L X 2010 Annals of Physics 325 2140 [34] Zhou B H, Huang Y C 2011 Physical Review D 84 047701 [35] Zhou B H, Huang Y C 2011 Physical Review A 84 032505 [36] Zhang Z L, Huang Y C 2014 Annals of Physics 342 143 [37] Zhang M L, Sun X T, Wang X X 2011 Chin. Phys. B 20 110202 [38] Jia L Q, Zhang M L, Wang X X 2012 Chin. Phys. B 21 070204 [39] Xue Y, Weng D W, Chen L Q 2013 Acta Phys. Sin. 62 044601(in Chinese) [薛纭, 翁德玮, 陈立群 2013 物理学报 62 044601] [40] Chen X W, Mei F X 2011 Chin. Phys. Lett. 28 40204 [41] Huang W L, Cai J L 2011 Chin. Phys. Lett. 28 110203

#### 施引文献

•  [1] Huang Y C Mechanics Research Communications 30 567 [2] Huang Y C, Li X G 2005 Acta Phys. Sin. 54 3473(in Chinese) [黄永畅, 李希国 2005 物理学报 54 3473] [3] Huang Y C, Li X G 2001 J. Nature 23 227(in Chinese) [黄永畅, 李希国 2001 自然杂志 23 227] [4] Yuan F F, Huang Y C 2013 Classical and Quantum Gravity 30 195008 [5] Ding G T 2009 Acta Phys. Sin. 58 3620(in Chinese) [丁光涛 2009 物理学报 58 3620] [6] Huang Y C, Huang C 2010 International Journal of Theoretical Physics 49 2320 [7] Huang Y C, Lee X G, Shao M X 2006 Modern Physics Letters A 21 1107 [8] Huang C, Huang Y C 2011 Physics Letters A 375 271 [9] Huang Y C, Liao L, Lee X G 2009 The European Physical Journal C 60 481 [10] Moore E N 1983 Theoretical Mechanics (New York: Wiley) [11] Fetter A L, Walecka J D 1980 Theoretical Mechanics of Particles and Continua (New York: McGraw-Hill, International series in pure and applied physics) [12] Mei F X 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔1991高等分析力学(北京: 北京理工大学出版社)] [13] Chetaev N G 1989 Theoretical Mechanics (Moscow: Mir Publishers) [14] Georgi H, Glashow S L 1974 Physical Review Letters 32 438 [15] Chen B 1987 Analytical Dynamics (Beijing: Peking University Press ) (in Chinese) [陈斌1987分析动力学(北京: 北京大学出版社)] [16] Wu D J 2013 Modern cosmology (Beijing: Tsinghua University Press) (in Chinese) [吴大江2013现代宇宙学(北京: 清华大学出版社)] [17] Nash C, Sen S 1983 Topology and Geometry for Physicists (London: Academic Press) [18] Pars L A 1965 A Treatise on Analytical Dynamics (London: Heinemann) [19] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York & London: Plenum) [20] Huang Y C, Jiang Y G, Lee X G 2007 Science in China G 50 339 [21] Zou P C, Huang Y C 2012 Physics Letters A 376 3575 [22] Peng Q H 1979 Chinese Science 3 274 [23] Tong Y 1981 Astronomical Journal 22 285 [24] Zheng X T, Tong Y 1984 Astronomical Journal 25 285 [25] Liao L, Huang Y C 2007 Physical Review D 75 025025 [26] Eichten E, Gottfried K, Kinoshita T, Lane K D, Yan T M 1980 Phys. Rev. D 21 203 [27] Liao L, Huang Y C 2007 Annals of Physics 322 2469 [28] Huang Y C, Yu C X 2007 Physical Review D 75 044011 [29] Yu C X, Huang Y C 2007 Physics Letters B 647 49 [30] Zhu Z, Yu H R 1997 Molecular structure and molecular potential energy function (Beijing: Science Press) [31] Huang Y C, Huo Q H 2008 Physics Letters B 662 290 [32] Huang Y C, Yang J L 2008 Physics Letters B 668 438 [33] Huang Y C, Yi L X 2010 Annals of Physics 325 2140 [34] Zhou B H, Huang Y C 2011 Physical Review D 84 047701 [35] Zhou B H, Huang Y C 2011 Physical Review A 84 032505 [36] Zhang Z L, Huang Y C 2014 Annals of Physics 342 143 [37] Zhang M L, Sun X T, Wang X X 2011 Chin. Phys. B 20 110202 [38] Jia L Q, Zhang M L, Wang X X 2012 Chin. Phys. B 21 070204 [39] Xue Y, Weng D W, Chen L Q 2013 Acta Phys. Sin. 62 044601(in Chinese) [薛纭, 翁德玮, 陈立群 2013 物理学报 62 044601] [40] Chen X W, Mei F X 2011 Chin. Phys. Lett. 28 40204 [41] Huang W L, Cai J L 2011 Chin. Phys. Lett. 28 110203
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##### 出版历程
• 收稿日期:  2014-03-13
• 修回日期:  2014-05-27
• 刊出日期:  2014-10-05

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