A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci
A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci
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In our eReader you can find the full English version of the book. Read A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci 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 A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci
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Thus we have either ji = o and y^ = o, giving a complete sphere, or else the relation given in the last equation of Art. 97. To interpret this relation, let aj> be the upper limiting curve. 128 CALCULUS OF VARIATLONS. P the point of intersection with the arc whose centre is c^py the ordinate y^ of the limiting curve, and np the normal. Then cpn = /„ and npy ~ n^, and we have r _ cos n^ ji cos tl (12) and this equation can only be satisfied by making cos t^ unity, which shows that the tangent to... the limiting curve at/ must be parallel to the axis of x ; that is, that j, must be either a maximum or . Minimum ordinate. But if y^ should become equal to r, this relation would no longer be necessary, for then the lines cp and yp would coincide, the angles cpn and ypn become the same angle cpn^ and (12) becomes merely T COS ci)7t - = £_, which determines nothing regardins: the direction r cos cp7i of the normal or tangent to the limiting curve ; and hence in this case the ordinate jj/^ need be neither a maximum nor a mini- mum.
What to read after A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci?
You can find similar books in the "Read Also" column, or choose other free books by Lewis Buffett Carll to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Thus we have either ji = o and y^ = o, giving a complete sphere, or else the relation given in the last equation of Art. 97. To interpret this relation, let aj> be the upper limiting curve. 128 CALCULUS OF VARIATLONS. P the point of intersection with the arc whose centre is c^py the ordinate y^ of the limiting curve, and np the normal. Then cpn = /„ and npy ~ n^, and we have r _ cos n^ ji cos tl (12) and this equation can only be satisfied by making cos t^ unity, which shows that the tangent to... the limiting curve at/ must be parallel to the axis of x ; that is, that j, must be either a maximum or . Minimum ordinate. But if y^ should become equal to r, this relation would no longer be necessary, for then the lines cp and yp would coincide, the angles cpn and ypn become the same angle cpn^ and (12) becomes merely T COS ci)7t - = £_, which determines nothing regardins: the direction r cos cp7i of the normal or tangent to the limiting curve ; and hence in this case the ordinate jj/^ need be neither a maximum nor a mini- mum.
What to read after A Treatise On the Calculus of Variations Arranged With the Purpose of Introduci?
You can find similar books in the "Read Also" column, or choose other free books by Lewis Buffett Carll to read onlineMoreLess
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