LONG Zixuan, ZHANG Yi. Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2013,52(5):51-56.
LONG Zixuan, ZHANG Yi. Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2013,52(5):51-56.DOI:
Based on the fractional integral extended by sine periodic law introduced by EI-Nabulsi
the fractional action-like Noether symmetries and conserved quantities for holonomic systems are studied. First
the fractional actionlike variational problem based on the fractional integral extended by sine periodic law is established
the fractional action-like d'Alembert-Lagrange principle is deduced
as well as the fractional action-like Euler-Lagrange equations is obtained. Secondly
the definitions and criteria of the fractional actionlike Noether's (quasi-) symmetrical transformations are presented in terms of the invariance of the fractional action-like Hamilton action under the infinitesimal transformations of group. Finally
fractional action-like Noether's theorem for holonomic systems is explored
the relationship between the Noether symmetry and the conserved quantity of the system is revealed
and two examples are given to illustrate the application of the results.
关键词
类分数阶Noether定理按正弦周期律拓展的分数阶积分类分数阶(准)对称变换守恒量
Keywords
fractional action-like Noether theoremfractional integral extended by sine periodic lawfractional action-like (quasi-) symmetric transformationconserved quantity