N. Sansonetto


Fasso F., Sansonetto N.
We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their "gauge-like" generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution.
Keywords: nonholonomic mechanical systems, conservation of energy, reaction-annihilator distribution, gauge momenta, nonholonomic Noether theorem
Citation: Fasso F., Sansonetto N.,  Conservation of Energy and Momenta in Nonholonomic Systems with Affine Constraints, Regular and Chaotic Dynamics, 2015, vol. 20, no. 4, pp. 449-462
Fasso F., Ramos A., Sansonetto N.
We consider nonholonomic systems with linear, time-independent constraints subject to ositional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution $\mathcal{R}^\circ$, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution $\mathcal{R}^\circ$. Since the fibers of $\mathcal{R}^\circ$ contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved omenta than what was known so far. Some examples are given.
Keywords: nonholonomic systems, first integrals, first integrals linear in the velocities, symmetries of nonholonomic systems, reaction forces, Noether theorem
Citation: Fasso F., Ramos A., Sansonetto N.,  On the Existence of Invariant Tori in Nearly-Integrable Hamiltonian Systems with Finitely Differentiable Perturbations, Regular and Chaotic Dynamics, 2007, vol. 12, no. 6, pp. 579-588
Fasso F., Giacobbe A., Sansonetto N.
It has been recently observed that certain (reduced) nonholonomic systems are Hamiltonian with respect to a rank-two Poisson structure. We link the existence of these structures to a dynamical property of the (reduced) system: its periodicity, with positive period depending continuously on the initial data. Moreover, we show that there are in fact infinitely many such Poisson structures and we classify them. We illustrate the situation on the sample case of a heavy ball rolling on a surface of revolution.
Keywords: Poisson structures, non-holonomic systems, periodic flows
Citation: Fasso F., Giacobbe A., Sansonetto N.,  Periodic flows, rank-two Poisson structures, and nonholonomic mechanics , Regular and Chaotic Dynamics, 2005, vol. 10, no. 3, pp. 267-284

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