Perturbation to Noether Symmetry and Adiabatic Invariants for Fractional Vakonomic Dynamics

Fractional calculus, due to its memory, global correlation and openness characteristics, provides a modeling method for dissipative systems. By embedding the constraint equations into the integrand function, vakonomic dynamics becomes a model for handling non-holonomic constraint problems. To study the dynamics of nonconservative nonholonomic systems, this paper investigates the perturbation of Noether symmetry and the adiabatic invariants for fractional vakonomic dynamics. Firstly, the fractional vakonomic dynamic equations are established by using a variational principle with embedded constraints. Secondly, the Noether symmetry and the conserved quantities of fractional vakonomic dynamics are given. Then the perturbation to symmetry and the adiabatic invariants for fractional vakonomic dynamics are studied. Finally, two examples are given to illustrate the application of the results.