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Usually there does not exist an integral invariant of Poincaré-Cartan's type for a nonholonomic system because a constraint submanifold does not admit symplectic structure in general. An integral variant of Poincaré-Cartan's type, depending on the nonholonomy of the constraints and nonconservative forces acting on the system, is derived from D'Alembert-Lagrange principle. For some nonholonomic constrained...
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