Deformable Asymmetric Tops under Similarity Transformations

Miguel, A. San

doi:10.1007/s00332-003-0539-z

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…For any affine mapping φ ∈ Aff(N, M ), an analogous representation is valid when the affine coordinates are fixed (i.e., origins of the reference frames and the linear bases) [7,10,19,20,[23][24][25][26][27][29][30][31][32][33][34][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][55][56][57][58]60]. Let us also quote the following 'representation' property of the operation L:…”

Section: Dynamics Of Affinely Rigid Bodiesmentioning

confidence: 99%

Classical Dynamics of Fullerenes

Sławianowski

Kotowski

2017

Z. Angew. Math. Phys.

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Abstract. The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.Mathematics Subject Classification. 74H99.

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Section: Dynamics Of Affinely Rigid Bodiesmentioning

confidence: 99%

Classical Dynamics of Fullerenes

Sławianowski

Kotowski

2017

Z. Angew. Math. Phys.

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“…is an element of the tensor space V ⊗ V ⋆ ≃ L(V ); Ω i j are spatial, or laboratoryreferred components. The co-moving (material) representation, mentioned in (28) for general (not necessarily affine) bodies is given by…”

Section: Affine Bodies Basic Geometry Symmetries and Canonical Formalismmentioning

confidence: 99%

“…We are aware also of the existence of some much earlier Russian papers (private information), however, having no explicit references we were unable to find them. Later on the subject developed rapidly both on the level of theory and applications and attracted the attention of many researchers [5] [7] [9] [11] [12] [18] [23] [27] [28] [29] [30] [31] [32] [35] [36] [38] [42] [43] [44] [45] [46] [52]. What concerns theory and mathematical foundations, deep studies by Burov and Chevalier [5] [7] are recommended.…”

Section: Introductionmentioning

confidence: 99%