Derivative of a vector function with nonfixed bases
Derivative of a vector function with nonfixed bases [ edit ] The above formulas for the derivative of a vector function rely on the assumption that the basis vectors e 1 , e 2 , e 3 are constant, that is, fixed in the reference frame in which the derivative of a is being taken, and therefore the e 1 , e 2 , e 3 each has a derivative of identically zero. This often holds true for problems dealing with vector fields in a fixed coordinate system, or for simple problems in physics . However, many complex problems involve the derivative of a vector function in multiple moving reference frames, which means that the basis vectors will not necessarily be constant. In such a case where the basis vectors e 1 , e 2 , e 3 are fixed in reference frame E, but not in reference frame N, the more general formula for the ordinary time derivative of a vector in reference fra...