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We consider Noether symmetries of the equations defined by the sections ofcharacteristic line bundles of nondegenerate 1-forms and of the associatedperturbed systems. It appears that this framework can be used fortime-dependent systems with constraints and nonconservative forces, allowing aquite simple and transparent formulation of the momentum equation and theNoether theorem in their general forms.

Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems