,A more useful means of expressing the coordinate functions is in terms of the change in coordinates. This will eventually lead to a scheme for expressing equations that are independent of any coordinate system, namely vector equations. To begin, we define the change in coordinates as a difference in coordinate values:
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which in turn can be rewritten in terms of a single function F via analytical manipulation:
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This function, whose parameters include both times t1 and t2, is an integral:
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with vx(t) being the new function whose only parameter is time. Additionally, the change in coordinates itself can also be written as an integral
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The limits of integration t1 and t2 are usually taken to be 0 seconds and some arbitrary time t respectively. Subsequeantly x1 becomes the value of the position at t=0, or x0, and x2 becomes the value of the position at time t, or just x, and thus the change in coordinates are written in the literature as
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| Other Examples | |
| Cylindrical Coordinates | Spherical Coordinates |
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