On the number  of weakly Noetherian constants of motion  ofnonholonomic systems

Francesco Fassò; Andrea Giacobbe; Nicola Sansonetto

doi:10.3934/jgm.2009.1.389

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2009, Volume 1, Issue 4: 389-416. Doi: 10.3934/jgm.2009.1.389

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On the number of weakly Noetherian constants of motion of nonholonomic systems

1.
Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova
2.
Università di Verona, Dipartimento di Informatica, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona

Received: September 2009

Revised: January 2010

Published: December 2009

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Abstract

We develop a method to give an estimate on the number of functionally independent constants of motion of a nonholonomic system with symmetry which have the so called 'weakly Noetherian' property [22]. We show that this number is bounded from above by the corank of the involutive closure of a certain distribution on the constraint manifold. The effectiveness of the method is illustrated on several examples.

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Mathematics Subject Classification: 37J15, 37J05, 70F25.

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