Affiliation:
1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China
2. School of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
Abstract
This research aims to investigate the Noether symmetry and conserved quantity for the fractional Lagrange system with nonholonomic constraints, which are based on the Herglotz principle. Firstly, the fractional-order Herglotz principle is given, and the Herglotz-type fractional-order differential equations of motion for the fractional Lagrange system with nonholonomic constraints are derived. Secondly, by introducing infinitesimal generating functions of space and time, the Noether symmetry of the Herglotz type is defined, along with its criteria, and the conserved quantity of the Herglotz type is given. Finally, to demonstrate how to use this method, two examples are provided.
Funder
Postgraduate Research and Practice Innovation Program of Jiangsu Province
National Natural Science Foundation of China
Reference46 articles.
1. Oldham, K.B., and Spanier, J. (1974). The Fractional Calculus, Academic Press.
2. Recent history of fractional calculus;Machado;Commun. Nonlinear Sci. Numer. Simulat.,2011
3. Podlubny, I. (1999). Fractional Differential Equations, Academic Press.
4. Lopes, A.M., and Chen, L.P. (2022). Fractional order systems and their applications. Fractal Fract., 6.
5. Nonconservative Lagrangian and Hamiltonian mechanics;Riewe;Phys. Rev. E,1996