Rigidity Triangles and Minors

Boris Albar

Description

Rigidity, Triangles and Minors Boris Albar I3M/LIRMM, Montpellier 3 Mai 2012 Rigidity, Triangles and Minors

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• incompressible bars

Informations

• Publié par: pefav
• Publié le: 01 mai 2012
• Nombre de lectures: 42
• Langue: English

Extrait

Rigidity,Trianglesdna BorisAlbar I3M/LIRMM,Montpellier iRig 3Mai2012 idyt,rTaignelsnadiMonsr Minors

Tensegrity iRigidyt ATensegritystructureisaphysicalsystemconsistingofafinitenumberof inextendablecablesandincompressiblebarslinkedtogetherbytheir extremities. Whichofthesestructuresare”stable”? iRigidyt,rTaignelsnadiMonsr

Tensegrity iRigidyt ATensegritystructureisaphysicalsystemconsistingofafinitenumberof inextendablecablesandincompressiblebarslinkedtogetherbytheir extremities. Whichofthesestructuresare”stable”? iRigidyt,rTaignelsnadiMonsr

Stress iRigidyt Givenaembeddingρ:V 7−→ R d ofagraphG=(V,E).Astressonρ isafunctionω:V × V → R suchthatforallu ∈ V: X ω( { u,v } )(ρ(v) − ρ(u))=0. { u,v }∈ E Definition LetG=(V,E)agraph.Anembeddingρ:V 7−→ R d ofGisd-stress freeifeverystressistrivial(ω=0). Definition Gisgenericallyd-stressfreeifthesetofalld-stressfreeembeddingsofG isopenanddenseinthesetofallembeddingsofG( ' R dn ). iRigidyt,rTaignelsnadiMonsr

Stress iRigidyt Givenaembeddingρ:V 7−→ R d ofagraphG=(V,E).Astressonρ isafunctionω:V × V → R suchthatforallu ∈ V: X ω( { u,v } )(ρ(v) − ρ(u))=0. { u,v }∈ E Definition LetG=(V,E)agraph.Anembeddingρ:V 7−→ R d ofGisd-stress freeifeverystressistrivial(ω=0). Definition Gisgenericallyd-stressfreeifthesetofalld-stressfreeembeddingsofG isopenanddenseinthesetofallembeddingsofG( ' R dn ). iRigidyt,rTaignelsnadiMonsr