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Unformatted text preview: Differentiation of vectors • In a Cartesian system, ˆ i , ˆ j , and ˆ k are fixed unit vectors • If we have a vector ~ A = A x ˆ i + A y ˆ j + A z ˆ k , where the components are functions of t , then we can take a derivative d ~ A dt = dA x dt ˆ i + dA y dt ˆ j + dA z dt ˆ k • For example, ~ A could be the position of a particle, and then the time derivative is the velocity. If ~ A is the velocity, then the time derivative is the acceleration. • What do we do if the vector is described in another coordinate systems that does not have fixed unit vectors? Patrick K. Schelling Introduction to Theoretical Methods Differentiation of vectors in a polar system • We can express ~ A in the xyplane using unit vectors in a polar system ~ A = A x ˆ i + A y ˆ j = A r ˆ e r + A θ ˆ e θ • The ˆ i and ˆ j unit vectors have a fixed direction, but ˆ e r and ˆ e θ do not Patrick K. Schelling Introduction to Theoretical Methods Unit vectors in polar coordinate system expressed in terms of Cartesian system • We can easily see that, ˆ e r = cos θ ˆ i + sin θ ˆ j ˆ e θ = sin θ ˆ i + cos...
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This note was uploaded on 07/30/2011 for the course PHZ 3113 taught by Professor Staff during the Spring '03 term at University of Central Florida.
 Spring '03
 Staff

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