Segel, Problem 1.3.1 (In Progress)

(1) Fi = mai (where i = subscript)
(2) F'i = ma'i (where ' denotes a change in coordinate system)
(13) Tqr = lqi*lrj*T'ij (where T = stress tensor and q,r,i,j are subscripts

  • Show that if (1) and (2) are consistent and if acceleration is a vector, then force is a vector. Follow the line of reasoning used to obtain (13).

    Calculations:

    Components of Fi and F'i are the projections of F on the fixed mutually perpendicular unit vectors e^(i) and e^(i)', respectively, and are thus only different notationally. (2) holds iff (1) holds

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    Problem posted 6/29/05 -- LAL