Mécanique Céleste Vol.1
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] COS. Ï — COS. [2 at -+- s)\= At. cos. s ^ ■ — • > •' ' ^ ' ''* 2a i 2a 5 .Ji^dt. COS. a t -\ . f(^dt . sm. at = — — . -\ — - — . l — sm. a t . sin. i -j- cos. a t . cos. s \ ; -id (_ y and by [22] Int. the coefficient of ^ is = sin. [{2 at -\- s) — a /] = sin. {a t -|- e), and tlie other coefficient — sin. a t . sin. e -\- cos. a t . cos. e = cos. (« ^ -|- e), hence the preceding expression becomes — — - . sin. {at -\-s) -\- — — . cos. (a t -\- e). These are the terms produced by Q = A", sin.... {mt -{- s), and by writing é * + s for s we obtain tliose arising from Q = K .cos. [i/it -{- s), namely, «AT , , , aKt as in [871', 871"].
~I^ ■ ^°^- (" ^ + '^ " Ta" • *^°^' ^" ' "^ '^' 122 486 INTEGRATION OF [Méc. Cél.
nothing. Taking the differentials of these values i — 1 times successively, we shall form the differential equations of the order i — 1,* [672] c = V ; c'=V' ; &c.
The coefficients of — -^, -,— , in the differentials of V, V, k.c., being the values of F, F', &;c., H, H', &c., we must substitute them in the differential functions [864'] [873] dt.(FQ + F'Q' + kc.) ; dt .
What to read after Mécanique Céleste Vol.1?
You can find similar books in the "Read Also" column, or choose other free books by Bowditch, N. I. (Nathaniel Ingersoll), 1805-1861 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
] COS. Ï — COS. [2 at -+- s)\= At. cos. s ^ ■ — • > •' ' ^ ' ''* 2a i 2a 5 .Ji^dt. COS. a t -\ . f(^dt . sm. at = — — . -\ — - — . l — sm. a t . sin. i -j- cos. a t . cos. s \ ; -id (_ y and by [22] Int. the coefficient of ^ is = sin. [{2 at -\- s) — a /] = sin. {a t -|- e), and tlie other coefficient — sin. a t . sin. e -\- cos. a t . cos. e = cos. (« ^ -|- e), hence the preceding expression becomes — — - . sin. {at -\-s) -\- — — . cos. (a t -\- e). These are the terms produced by Q = A", sin.... {mt -{- s), and by writing é * + s for s we obtain tliose arising from Q = K .cos. [i/it -{- s), namely, «AT , , , aKt as in [871', 871"].
~I^ ■ ^°^- (" ^ + '^ " Ta" • *^°^' ^" ' "^ '^' 122 486 INTEGRATION OF [Méc. Cél.
nothing. Taking the differentials of these values i — 1 times successively, we shall form the differential equations of the order i — 1,* [672] c = V ; c'=V' ; &c.
The coefficients of — -^, -,— , in the differentials of V, V, k.c., being the values of F, F', &;c., H, H', &c., we must substitute them in the differential functions [864'] [873] dt.(FQ + F'Q' + kc.) ; dt .
What to read after Mécanique Céleste Vol.1?
You can find similar books in the "Read Also" column, or choose other free books by Bowditch, N. I. (Nathaniel Ingersoll), 1805-1861 to read onlineMoreLess
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