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Unformatted text preview: the components of a quantity such as a vector with respect to coordinate transformations. A set of independent variables x 1 , 2 2 , 2 3 may be thought of as specifying the coordinates of a point in a frame of reference. A transformation from q r 2 2 , x 3 to a set of new variables 2 1 , 3 2 , 2 3 through the equations specifies a transformation of coordinates. The inverse transformation (2) xi = gi(Z1, 2 2 1 33) i = 1,2,3, proceeds in the reverse direction. In order to insure that such a transforma tion is reversible and in onetoone correspondence in a certain region R of the variables ( q , 2 2 , z 3 ) , i.e., in order that each set of numbers (XI, 2 2 , ~ ) defines a unique set of numbers ( 2 1 , 3 2 , 2 3 ) , for (XI, 2 2 , ~ ~ ) in the region R,...
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 Fall '05
 Thomson

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