Periodic Orbits

Cover Periodic Orbits
Periodic Orbits
Forest Ray Moulton
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. , p. ; 4, . . . , 0. And the properties of equations (11) that F u+l (r) is a sum of cosines of integral multiples of T, and that G n+ i(r) is a sum of sines of integral multiples of T. Hence they may be written in the form FH. , (T) = 2 A**" COSJr, (?. +, (T) = 2 B^ Bin jr.
In order that the solution of the first equation of (42) shall be periodic the condition = (43) must be imposed, and this condition uniquely determines a, _, .
After equation (43) has been satisfied, the solution of the f
...irst equation of (42) is I = o. +l - M6. _, 8in2r+2 a^" cos jr.

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