Noether Theorem For Fractional Constrained Mechanical Systems

The dynamical system occupies an important position in modern mathematics,mechanics,physics and other disciplines.It is important to study it.This paper researchs Noether's quasi-symmetry theorems for constrained mechanical systems and fractional constrained mechanical systems,respectively based on the special infinitesimal group of transformations without transforming time and the general infinitesimal group of transformations with transforming time by using time-reparameterization method.This paper is divided into five chapters.In the first chapter,the development of Noether symmetry theorems and fractional calculus and the research background and significance of the subject are briefly discussed.The main research contents and work of this paper are introduced.In the second chapter,the author introduces the related definitions,formulas and properties of fractional calculus and fractional conservation.In the third chapter,the Noether's quasi-symmetry and conserved quantity theorems for fractional Lagrange system are studied.The Noether's quasi-symmetry and conserved quantity theorems for the Lagrange system are proved by using time-reparameterization method.On the basis,the Noether's quasi-symmetry and conserved quantity theorems for the fractional Lagrange system are researched.The Noether's quasi-symmetry for the fractional Lagrange system is defined and the respectively conserved quantities are obtained.In the fourth chapter,the Noether's quasi-symmetry and conserved quantity theorems for fractional Hamilton system are studied.The Noether's quasi-symmetry and conserved quantity theorems for the Hamilton system are proved by using time-reparameterization method.On the basis,the Noether's quasi-symmetry and conserved quantity theorems for the fractional Hamilton system are researched.The Noether's quasi-symmetry for the fractional Hamilton system is defined and the respectively conserved quantities are obtained.In the fifth chapter,the Noether's quasi-symmetry and conserved quantity theorems for fractional generalized Birkhoff system are studied.The Noether's quasi-symmetry and conserved quantity theorems for the generalized Birkhoff system are proved by using time-reparameterization method.On the basis,the Noether's quasi-symmetry and conserved quantity theorems for the fractional generalized Birkhoff system are researched.The Noether's quasi-symmetry for the fractional generalized Birkhoff system is defined and the respectively conserved quantitiesare obtained.Finally,conclusions and prospects are given.