Nonholonomic constraints with fractional derivatives. (English) Zbl 1101.70011
Summary: We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives, and provide some examples. The corresponding equations of motion are derived using variational principle. We prove that fractional constraints can be used to describe the evolution of dynamical systems in which some coordinates and velocities are related to velocities through a power-law memory function.
MSC:
70F25 | Nonholonomic systems related to the dynamics of a system of particles |
70H03 | Lagrange’s equations |
70H25 | Hamilton’s principle |
26A33 | Fractional derivatives and integrals |