Abstract
Nonholonomic dynamics describes systems constrained by nonintegrable relationships. The constraint, called holonomic constraint, depends only on the coordinates. It does not depend on the velocities. Velocity dependent constraints such as could be holonomic constraints if it can be integrated into a simple holonomic constraint. A constraint that cannot be integrated into a holonomic constraint is called non-holonomic (Tchetaev, 1962; Dobronravov, 1970; Rumiantsev, 1978, 2000, 1982). The constraint, called fractional nonholonomic constraint (Tarasov and Zaslavsky, 2006a), depends on the derivatives of non-integer orders (Samko et al., 1993; Kubas et al., 2006). The fractional nonholonomic constraints are interpreted as constraints with long-term memory (Tarasov and Zaslavsky, 2006a). Fractional derivatives allow one to describe constraints with power-law long-term memory by using the fractional calculus (Samko et al., 1993; Kubas et al., 2006).
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Tarasov, V.E. (2010). Fractional Nonholonomic Dynamics. In: Fractional Dynamics. Nonlinear Physical Science, vol 0. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14003-7_17
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