Mathematical Physics/Mathematical Problems in Mechanics
Nonlocal orientation-dependent dynamics of charged strands and ribbons
[Dynamique non-locale des filaments électisés]

Présenté par : Charles-Michel Marle

Holm, Darryl D.1 ; Putkaradze, Vakhtang2, 3
1 Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2 Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
3 Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA
Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1093-1098.

Nous établir les équations de la dynamique hamiltonienne d'une courbe (chaine moléculaire) dans l'espace physique R3 sujette á des interactions élastiques ainsi que non-locales (électrostatiques par exemple). Les équations dynamiques des variables réduites par symétrie sont écrites sur l'espace dual de l'algèbre de Lie so(3)Ⓢ(R3⊕R3⊕R3⊕R3) (produit semidirect) avec trois 2-cocycles. Nous démontrons aussi que l'interaction non-locale produit un nouvel terme intéressant, qui dérive de l'action coadjointe du group de Lie SO(3) sur son algébre so(3). Les nouvelles équations du filament sont écrites sous une forme conservative grâce aux actions coadjointes correspondantes.

Time-dependent Hamiltonian dynamics is derived for a strand of charged units in R3 held together by both nonlocal (for example, electrostatic) and elastic interactions. The dynamical equations in the symmetry-reduced variables are written on the dual of the semidirect-product Lie algebra so(3)Ⓢ(R3⊕R3⊕R3⊕R3) with three 2-cocycles. We also demonstrate that the nonlocal interaction produces an interesting new term deriving from the coadjoint action of the Lie group SO(3) on its Lie algebra so(3). The new strand equations are written in conservative form by using the corresponding coadjoint actions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.06.009
Holm, Darryl D. 1 ; Putkaradze, Vakhtang 2, 3

1 Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2 Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
3 Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131, USA 
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     title = {Nonlocal orientation-dependent dynamics of charged strands and ribbons},
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Holm, Darryl D.; Putkaradze, Vakhtang. Nonlocal orientation-dependent dynamics of charged strands and ribbons. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1093-1098. doi : 10.1016/j.crma.2009.06.009. https://www.numdam.org/articles/10.1016/j.crma.2009.06.009/

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