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The Differential Line Vector for Coordinate (微分行向量的坐标).pdf

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9/6/2005 The Differential Line Vector for Coordinate Systems.doc 1/3 The Differential Displacement Vector for Coordinate Systems Let’s determine the differential displacement vectors for each coordinate of the Cartesian, cylindrical and spherical coordinate systems! Cartesian This is easy! d r ⎡ d x d y d z ⎤ ⎛ ⎞ ˆ ⎛ ⎞ ˆ ⎛ ⎞ ˆ dx dx a + a + a dx ⎢⎜ ⎟ x ⎜ ⎟ y ⎜ ⎟ z ⎥ dx dx dx dx ⎣⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎦ ˆ a dx x ⎡⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎤ d r d x ˆ d y ˆ d z ˆ dy dy ⎢ a + a + a ⎥dy ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ dy ⎢ dy x dy y dy z ⎥ ⎣⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎦ aˆ dy y d r ⎡ d x d y d z ⎤ ⎛ ⎞ ˆ ⎛ ⎞ ˆ ⎛ ⎞ ˆ dz dz a + a + a dz ⎢⎜ ⎟ x ⎜ ⎟ y ⎜ ⎟ z ⎥ dz dz dz dz ⎣⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎦ ˆ a dz z Jim Stiles The Univ. of Kansas Dept. of EECS 9/6/2005 The Differential Line Vector for Coordinate Systems.doc 2/3 Cylindrical Likewise, recall from the last handout that: ˆ d ρ aρ d ρ Maria, look! I’m starting to see a trend! d r ˆ dx dx a dx dx
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