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December  2009, 1(4): 389-416. doi: 10.3934/jgm.2009.1.389

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

Francesco Fassò 1, , Andrea Giacobbe 1, and  Nicola Sansonetto 2,

1. 

Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova, Italy, Italy
2. 

Università di Verona, Dipartimento di Informatica, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy

Received  September 2009 Revised  January 2010 Published  January 2010

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.
Keywords: Constants of motion, Noether theorem., Nonholonomic systems, First integrals.
Mathematics Subject Classification: 37J15, 37J05, 70F2.
Citation: Francesco Fassò, Andrea Giacobbe, Nicola Sansonetto. On the number of weakly Noetherian constants of motion of nonholonomic systems. Journal of Geometric Mechanics, 2009, 1 (4) : 389-416. doi: 10.3934/jgm.2009.1.389
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