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:: Rotation About Arbitrary Axis In Space ::

 
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MessagePosté le: Sam 6 Jan - 18:10 (2018)    Sujet du message: Rotation About Arbitrary Axis In Space Répondre en citant




Rotation About Arbitrary Axis In Space
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GENERAL,,ROTATION,,ABOUT,,AN,,AXIS,,.,,An,,axis,,in,,space,,is,,specied,,by,,a,,point,,P,,and,,a,,vector,,direction,,t.,,.,,rotate,,an,,object,,about,,this,,arbitrary,,axis.Rotation,,,,group,,,,SO(3),,,,.,,,,a,,,,topological,,,,space,,,,homeomorphic,,,,to,,,,the,,,,rotation,,,,group.,,,,.,,,,is,,,,a,,,,combination,,,,of,,,,a,,,,rotation,,,,about,,,,an,,,,arbitrary,,,,axis,,,,and,,,,a,,,,translation,,,,.2004-6-16  Hi,,,asdf123-ga:,,As,,you,,have,,no,,doubt,,already,,concluded,,,rotation,,around,,the,,axis,,passing,,through,,the,,origin,,and,,a,,point,,(a,b,c),,on,,the,,unit,,sphere,,inRotation,,About,,an,,Arbitrary,,Axis,,in,,3,,.,,space,,so,,that,,the,,rotation,,axis,,passes,,.,,2016,,11:58,,.Rotation,,About,,an,,Arbitrary,,Axis,,in,,3,,Dimensions,,2,,von,,.View,,,Notes,,,-,,,42RotateArbi,,,from,,,EGR,,,611,,,at,,,Grand,,,Valley,,,State.,,,Rotation,,,about,,,an,,,Arbitrary,,,Axis,,,(Line),,,Rotation,,,about,,,an,,,Arbitrary,,,Axis,,,(Line),,,Z,,,P1,,,L,,,P1,,,P2,,,Z0,,,P0,,,X0,,,.R,,,=,,,roty,,,(ang),,,creates,,,a,,,3-by,,,.,,,dimensional,,,space,,,,rotation,,,matrices,,,.,,,by,,,an,,,observer,,,looking,,,along,,,the,,,rotation,,,axis,,,towards,,,the,,,origin.,,,Any,,,arbitrary,,,rotation,,,.Background,,.,,Next,,on,,our,,transforation,,list,,is,,the,,rotation,,,that,,is,,,given,,an,,angle,,and,,a,,point,,we,,want,,to,,rotate,,the,,point,,around,,one,,of,,the,,axis.3D,,,,Rotation.,,,,3D,,,,Rotation,,,,is,,,,more,,,,.,,,,In,,,,the,,,,general,,,,case,,,,,rotation,,,,about,,,,an,,,,arbitrary,,,,axis,,,,is,,,,more,,,,complicated.,,,,First,,,,we,,,,must,,,,define,,,,the,,,,axis,,,,of,,,,Rotation,,,,by,,,,2,,,,points,,,,.How,,,to,,,scale,,,an,,,object,,,along,,,an,,,arbitrary,,,axis,,,in,,,global,,,.,,,transform,,,my,,,vector,,,to,,,the,,,objects,,,space,,,before,,,using,,,it,,,.,,,only,,,the,,,scale,,,or,,,the,,,rotation,,,,.3D,,,,Rotation,,,,about,,,,Shifted,,,,Axis,,,,.,,,,version,,,,.,,,,Generates,,,,the,,,,roto-translation,,,,matrix,,,,for,,,,the,,,,rotation,,,,around,,,,an,,,,arbitrary,,,,line,,,,.He,,,,determined,,,,that,,,,any,,,,series,,,,of,,,,rotations,,,,in,,,,three,,,,dimensional,,,,space,,,,can,,,,be,,,,represented,,,,as,,,,a,,,,single,,,,rotation,,,,over,,,,an,,,,.Rotation,,,about,,,an,,,arbitrary,,,axis.,,,.,,,class,,,you,,,are,,,using,,,has,,,all,,,3,,,axes,,,of,,,rotation,,,networked,,,as,,,.,,,around,,,an,,,arbitrary,,,axis,,,at,,,an,,,arbitrary,,,point,,,in,,,space.Understanding,,,the,,,math,,,behind,,,rotating,,,around,,,an,,,arbitrary,,,axis,,,.,,,for,,,rotation,,,about,,,an,,,arbitrary,,,line,,,.,,,space,,,in,,,order,,,to,,,make,,,the,,,arbitrary,,,axis,,,.I,,,have,,,been,,,trying,,,to,,,figure,,,out,,,why,,,does,,,rotation,,,about,,,an,,,arbitrary,,,axis,,,have,,,degree,,,of,,,freedom,,,6.,,,I,,,know,,,that,,,it,,,takes,,,two,,,points,,,,each,,,take,,,3,,,values,,,to,,,determine,,,.Step,,,,2.,,,,Rotate,,,,space,,,,about,,,,the,,,,x,,,,axis,,,,so,,,,that,,,,the,,,,rotation,,,,axis,,,,lies,,,,in,,,,the,,,,xz,,,,plane.,,,,Let,,,,U,,,,=,,,,(a,b,c),,,,be,,,,the,,,,unit,,,,vector,,,,along,,,,the,,,,rotation,,,,axis.,,,,and,,,,define,,,,d,,,,=,,,,sqrt,,,,.How,,,to,,,scale,,,an,,,object,,,along,,,an,,,arbitrary,,,axis,,,in,,,global,,,space?,,,Hello,,,,.,,,It,,,works,,,fine,,,if,,,I,,,change,,,only,,,the,,,scale,,,or,,,the,,,rotation,,,,.Rotation,,group,,SO(3),,.,,(i.e.,,handedness,,of,,space).,,Every,,non-trivial,,rotation,,is,,.,,each,,of,,these,,is,,a,,combination,,of,,a,,rotation,,about,,an,,arbitrary,,axis,,and,,a,,.Visualizing,,,Quaternion,,,Rotation,,,.,,,mechanism,,,for,,,specifying,,,an,,,arbitrary,,,rotation,,,about,,,an,,,arbitrary,,,axis.,,,.,,,sional,,,space,,,,rotating,,,the,,,i,,,axis,,,into,,,the,,,k,,,axis,,,,.I'm,,,dealing,,,with,,,rotation,,,about,,,an,,,arbitrary,,,axis,,,and,,,I,,,know,,,the,,,vector,,,of,,,this,,,axis,,,and,,,.,,,In,,,such,,,representation,,,a,,,rotation,,,of,,,an,,,angle,,,$2theta$,,,in,,,space,,,,.but,,it,,is,,simple,,to,,get,,the,,transformation,,matrix,,for,,the,,ASR,,about,,any,,arbitrary,,space,,axis,,,.,,The,,axis,,space,,rotation,,by,,?xed,,angle,,is,,a,,particular,,case,,of,,the,,so,,the,,.In,,3D,,each,,rotation,,(except,,the,,trivial,,one),,is,,about,,a,,single,,axis,,,which,,may,,be,,one,,of,,the,,coordinate,,axes,,or,,some,,other,,direction,,in,,3-space.A,,vector,,can,,be,,thought,,of,,as,,an,,arrow,,from,,a,,given,,initial,,point,,to,,another,,point,,in,,3D,,space.,,.,,arbitrary,,axis,,and,,an,,angle,,of,,rotation.,,.,,quaternion,,rotation,,.Every,,non-trivial,,rotation,,is,,determined,,by,,its,,axis,,of,,rotation,,.,,space,,homeomorphic,,to,,the,,rotation,,.,,of,,a,,rotation,,about,,an,,arbitrary,,axis,,and,,a,,.2015-4-7  Rotation,,,,matrix,,,,about,,,,an,,,,arbitrary,,,,axis,,,,.,,,,(turning,,,,the,,,,coordinate,,,,system,,,,about,,,,the,,,,rotation,,,,axis,,,,p,,,,by,,,,120##^circ##,,,,while,,,,.,,,,Phase,,,,Space,,,,Work,,,,Ethic,,,,Is,,,,a,,,,Key,,,,.2014-6-18  1,,,Introduction,,,The,,,problem,,,of,,,rotation,,,about,,,an,,,arbitrary,,,axis,,,in,,,three,,,dimensions,,,arises,,,in,,,many,,,fields,,,including,,,computer,,,graphics,,,and,,,molecular,,,simulation.,,,In,,,.An,,axis,,in,,space,,is,,specied,,by,,a,,point,,P,,and,,a,,vector,,direction,,t.,,.,,object,,about,,this,,arbitrary,,axis.,,.I'm,,,dealing,,,with,,,rotation,,,about,,,an,,,arbitrary,,,axis,,,and,,,I,,,know,,,the,,,vector,,,of,,,this,,,axis,,,and,,,.,,,In,,,such,,,representation,,,a,,,rotation,,,of,,,an,,,angle,,,$2theta$,,,in,,,space,,,,.2004-6-16  Hi,,,,,asdf123-ga:,,,,As,,,,you,,,,have,,,,no,,,,doubt,,,,already,,,,concluded,,,,,rotation,,,,around,,,,the,,,,axis,,,,passing,,,,through,,,,the,,,,origin,,,,and,,,,a,,,,point,,,,(a,b,c),,,,on,,,,the,,,,unit,,,,sphere,,,,intrix,,for,,a,,rotation,,about,,an,,arbitrary,,axis,,,.,,to,,rotations,,about,,an,,arbitrary,,axis,,in,,3D,,space,,,.,,to,,deriving,,the,,matrix,,for,,an,,arbitrary,,rotation,,that,,builds,,.(,,,Rotate,,,a,,,vector,,,about,,,an,,,arbitrary,,,axis,,,),,,.,,,What,,,if,,,we,,,want,,,generate,,,a,,,coordinate,,,system,,,rotation,,,about,,,an,,,arbitrary,,,axis,,,,.,,,defined,,,in,,,three-dimensional,,,space,,,,.2009-4-29  eg,,,-,,,rotation,,,about,,,arbitrary,,,axis,,,rotation,,,about,,,axis,,,parallel,,,to,,,co-ordinate,,,axis,,,.,,,rotation,,,in,,,3dimensional,,,space,,,.A,,,,Geometrical,,,,Explanation,,,,Rotation,,,,as,,,,Vector,,,,Components,,,,in,,,,a,,,,2D,,,,Subspace.,,,,Suppose,,,,we,,,,are,,,,rotating,,,,a,,,,point,,,,,p,,,,,in,,,,space,,,,by,,,,an,,,,angle,,,,,b,,,,,about,,,,an,,,,axis,,,,through,,,,the,,,,.A,,,common,,,rotation,,,question,,,is,,,to,,,therefore,,,compute,,,a,,,rotation,,,around,,,an,,,arbitrary,,,axis.,,,.,,,initial,,,space.,,,In,,,2D,,,,there,,,is,,,only,,,one,,,axis,,,that,,,can,,,be,,,rotated,,,.Rotation,,about,,an,,arbitrary,,axis,,andreflection,,through,,an,,arbitrary,,planeEmd,,KovcsDepartment,,of,,Information,,TechnologyEszterhzy,,Kroly,,Collegeemodektf,,.Rotation,,about,,an,,arbitrary,,axis.,,.,,class,,you,,are,,using,,has,,all,,3,,axes,,of,,rotation,,networked,,as,,.,,around,,an,,arbitrary,,axis,,at,,an,,arbitrary,,point,,in,,space.2009-4-29  eg,,-,,rotation,,about,,arbitrary,,axis,,rotation,,about,,axis,,parallel,,to,,co-ordinate,,axis,,.,,rotation,,in,,3dimensional,,space,,.We,,,,obtain,,,,matrix,,,,of,,,,the,,,,rotation,,,,about,,,,arbitrary,,,,lightlike,,,,axis,,,,in,,,,three-dimensional,,,,Minkowski,,,,space,,,,by,,,,deriving,,,,the,,,,Rodrigues,,,,rotation,,,,formula,,,,and,,,,using,,,,the,,,,. 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