Mathematical Theories of Planetary Motions
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In our eReader you can find the full English version of the book. Read Mathematical Theories of Planetary Motions Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Mathematical Theories of Planetary Motions
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we get Now d*x ^ d ( dx ^ \ dx ^dx d ( dx ^ ~\ ^f dx~\ z _ _ o 'y* < I (j / y* I o I o'Y* I -"t o I I df ~dt\. Dt J dt dt~dt\~dt J \. Dt J ' The preceding equation, therefore, becomes and hence, on integration with respect to t, between the limits t' and t, (25) t t = 8(U+T)dt = d (U+T)dt. This equation, in which dx it ... Denote any selected infini- tesimal variations, was Hamilton's starting point. The coordinates and velocities are functions of the time and of 6n constants. For the initial values of these, corresponding to the time f, we shall take a?/, j//, /, u-, v-, w- so that the final equations take the form (26) *, = *, (*/, 2//, zS, . . . <, vj, w/, . . . (tf) ). By the differentation of (26) with respect to t, we at once obtain (27) u f = u^xi, 2/j', zS, . . . W/, <, w^, ... (tt')). H NOT CONTAINING THE TIME. 129 The action t '=2 I = 2 / Tdt t> then takes the form (28) V = V(x l f . . . HI ... (t t r ) ). We will transform (28), by obtaining u', v', w r from (26) and sub- stituting them in it.
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You can find similar books in the "Read Also" column, or choose other free books by Otto Dziobek to read online
To quickly assess the difficulty of the text, read a short excerpt:
we get Now d*x ^ d ( dx ^ \ dx ^dx d ( dx ^ ~\ ^f dx~\ z _ _ o 'y* < I (j / y* I o I o'Y* I -"t o I I df ~dt\. Dt J dt dt~dt\~dt J \. Dt J ' The preceding equation, therefore, becomes and hence, on integration with respect to t, between the limits t' and t, (25) t t = 8(U+T)dt = d (U+T)dt. This equation, in which dx it ... Denote any selected infini- tesimal variations, was Hamilton's starting point. The coordinates and velocities are functions of the time and of 6n constants. For the initial values of these, corresponding to the time f, we shall take a?/, j//, /, u-, v-, w- so that the final equations take the form (26) *, = *, (*/, 2//, zS, . . . <, vj, w/, . . . (tf) ). By the differentation of (26) with respect to t, we at once obtain (27) u f = u^xi, 2/j', zS, . . . W/, <, w^, ... (tt')). H NOT CONTAINING THE TIME. 129 The action t '=2 I = 2 / Tdt t> then takes the form (28) V = V(x l f . . . HI ... (t t r ) ). We will transform (28), by obtaining u', v', w r from (26) and sub- stituting them in it.
What to read after Mathematical Theories of Planetary Motions?
You can find similar books in the "Read Also" column, or choose other free books by Otto Dziobek to read online
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