LA PROPAGAZIONE DELL'ERRORE - Circe

2 1 2 2 2 2 2 22 2( ) [ dS 2sen1d1sen1d3sen22d 1d2 sen1sen2d2sen24]1 2 2 2 2 2 2 2 2 1 2[( d1d2cos α1) σα ( d2d3cos α2)σα ] d1d 2d3 cosα1cosα2Cαα421{[ ( d1 d ) α ( d d ) α d d α α ]2 2 2 2 1 2 2 3 2 2 2= + sen + + sen 2 + 2 1 2 sen 1 sen 2 σd+42 2 2 2 2 2 2 2 2+ ( d1d2cos α1) σα + ( d2d3cos α2) σ + 2d 1d 2d 3cos1cos2C1 αα α2 αα 1 2}2σ = α + α + α + α α + α σ ++ + + =1 2 1 2dLa propagazione dell’errore 22Occorre calcolare σ, σ ,Cα1 α 2 α1α22 2α1 = l 2 − l 1 → σα= 2σl , α2 = l 3 − l 2 → σα= 2σlCVV( )= M V Vα1α2 α1 α21∂α1∂α1= Vl + Vl → Vα= Vl − Vl∂l2∂l1∂α2∂α2= Vl + Vl → Vα= Vl − Vl∂l∂lα 1 2 1 1 2 1[ ] ( )( ) ( )( )2 2α 3 2 2 3 2322 2 2l l l l l l lM V α V α= M V − V V − V = M − V = − σ = − σ1 2 2 1 3 2 2 22La σ( S ) diventa allora:2 1 2 2 2 2 2 22 2( ) [ dS 2sen1d1sen1d3sen22d 1d 2sen1sen2d2sen24]1 2 2 2 2 2 2 2 2 2( d1d2α1) σl ( d2d 3α2) σl ( d1d 2d3 α1 α2) σl4 2 cos 2 cos 2 cos cos1 2 2 2 2 2 22= [( d 1 + d 2 ) sen α1 + ( d 2 + d 3 ) sen α2 + 2d 1d2 senα1 senα2] σd+41 2 2 2 2 22+ d2 [ d1cos α1 + d3cos α2 −d1d 3cos α1 cos α2] σl2σ = α + α + α + α α + α σ +22[ ]+ + − =2d