Noether theorem and first integrals of constrained Lagrangean systems

Abstract: The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this paper it is shown that every constant of the motion obtained from the Noether theorem is a first integral; thus, Noether theorem can be used for an effective integration of the corresponding distribution.

Keywords: Lagrangean system, Lepagean two-form, Euler-Lagrange form, singular Lagrangian, constrained system, Noether theorem, symmetry, constant of the motion, first integral.

Classification (MSC2000): 58F05, 70H35

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