For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are stu...For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.展开更多
水化作用后的网纹红土强度演变研究对其污染修复具有重要意义。文章基于不同质量分数HCl、CaO和NaCl水化作用后的网纹红土直剪试验和扫描电子显微镜(scanning electron microscope,SEM)试验,探讨了水化作用后的网纹红土强度和微结构演...水化作用后的网纹红土强度演变研究对其污染修复具有重要意义。文章基于不同质量分数HCl、CaO和NaCl水化作用后的网纹红土直剪试验和扫描电子显微镜(scanning electron microscope,SEM)试验,探讨了水化作用后的网纹红土强度和微结构演化规律。研究结果表明:HCl、CaO和NaCl水化作用后的网纹红土呈现不同的特征和累积效应,低质量分数HCl水化作用可使土体强度和黏聚力增大,但当质量分数大于5.7%后可引起强度和黏聚力骤降,内摩擦角则表现为始终增大;经CaO水化作用后的土体强度参数则随着CaO质量分数的增大而增大,但质量分数大于3%后的变化值相对明显;而经NaCl水化作用后的强度参数总体呈现下降趋势,但当质量分数超过8.4%后,呈现平稳趋势。同时发现经NaCl、CaO和HCl污染后的网纹红土微结构特点不同,表明水化作用引起的宏观力学特征与其微结构变化密切相关,研究结果为污染网纹红土的修复提供了依据。展开更多
基金supported by the National Natural Science Foundation of China(No.11272227)
文摘For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.
文摘水化作用后的网纹红土强度演变研究对其污染修复具有重要意义。文章基于不同质量分数HCl、CaO和NaCl水化作用后的网纹红土直剪试验和扫描电子显微镜(scanning electron microscope,SEM)试验,探讨了水化作用后的网纹红土强度和微结构演化规律。研究结果表明:HCl、CaO和NaCl水化作用后的网纹红土呈现不同的特征和累积效应,低质量分数HCl水化作用可使土体强度和黏聚力增大,但当质量分数大于5.7%后可引起强度和黏聚力骤降,内摩擦角则表现为始终增大;经CaO水化作用后的土体强度参数则随着CaO质量分数的增大而增大,但质量分数大于3%后的变化值相对明显;而经NaCl水化作用后的强度参数总体呈现下降趋势,但当质量分数超过8.4%后,呈现平稳趋势。同时发现经NaCl、CaO和HCl污染后的网纹红土微结构特点不同,表明水化作用引起的宏观力学特征与其微结构变化密切相关,研究结果为污染网纹红土的修复提供了依据。
