Similarly we have for the force acting on from ,
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(15)
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We will now introduce simultaneous coordinates. Let these be for time —
and
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In the equations of motion of , i.e. in the expression (14), we must use the coordinates and velocities of for the time defined by
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and we have
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In (15) we must use the coordinates and velocities of for the time defined by
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and we have
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Further, we have for use in (14)—
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and in (15)—
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The expression for is the same in both cases.
We find then,
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(16)
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This form of the equations is not unique. We can multiply by any power of , or make more complicated alterations, for which the reader is referred to Poincaré.
Multiplying by we get—
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(17)
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