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Geometric degree of non conservativeness

Jean Lerbet 1 Noël Challamel 2 François Nicot 3 Félix Darve 4, 5
1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne
3 IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture
4 3SR - Laboratoire sols, solides, structures - risques [Grenoble]
5 GéoMécanique
3SR - Laboratoire sols, solides, structures - risques [Grenoble]
Abstract : Symplectic structure is powerful especially when it is applied to Hamiltonian systems. We show here how this symplectic structure may define and evaluate an integer index that measures the defect for the system to be Hamiltonian. This defect is called the Geometric Degree of Non Conservativeness of the system. Darboux theorem on differential forms is the key result. Linear and non linear frameworks are investigated.
Keywords : Kinematic constraints Symplectic geometry Hamiltonian system Geometric Degree of Non Conservativeness
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https://hal.archives-ouvertes.fr/hal-01658202
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Submitted on : Monday, November 11, 2019 - 7:21:21 PM
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CNRS | IBISC-SIBI | IBISC | UNIV-EVRY | IRSTEA | UNIV-BREST | 3S-R | LIMATB | INRAE | UGA

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Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Geometric degree of non conservativeness. 3rd International Conference on Geometric Science of Information (GSI 2017), Nov 2017, Paris, France. pp.355--358, ⟨10.1007/978-3-319-68445-1_41⟩. ⟨hal-01658202⟩

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