Abstract
In this paper, the problem of first integrals of a nonholonomic system is discussed. The aim of this work is concentra.ted on finding the condition for existence of first integrals. The obtained results are applied for the construction of linear and quadratic integrals of nonholonomic systems. It obtains two important affirmations; they are: Any first integral could be treated as a particular nonholonomic constraint and contrarily, any nonholonomic constraint could be regarded as a first integral of the nonholonomic system.
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