396
Prof. de Sitter, On the bearing of the Principle
LXXI. 5,
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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