Geometric Properties Completely Characterizing All the Curves in a Plane Along W
Geometric Properties Completely Characterizing All the Curves in a Plane Along W
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In our eReader you can find the full English version of the book. Read Geometric Properties Completely Characterizing All the Curves in a Plane Along W 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 Geometric Properties Completely Characterizing All the Curves in a Plane Along W
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Substituting the values from (45) in (46), we obtain Solving this for B2, making a slight change in notation, we obtain B2 = Hiy"-{-H2, where Hi and H2 are arbitrary functions of x, y, 3^.
All the quadruply infinite systems having properties I, II, III are then defined by the differential equation 2/"^ = ^ y'"^ + ili^y" + H2)y'" + Bz, (47) where Hi and H2 are arbitrary functions of x, y, y' and B% is an arbitrary function of x, y, y', y" .
Section 4- Conversion of Property IV. In order to conve...rt Theorem IV, we state it in a form which does not assume the existence of a force, as follows: At each point {x, y) of the plane, there exists a certain direction of slope co(x, y) svxih that the sine of twice the angle this direction makes with the given element is equal to three times the tangent of the angle the given element makes with the parabola corresponding to it by theorem III.
CONVERSION OF PROPERTIES. 17 The parabola corresponding, in accordance with property III, to the 00 2 curves of system (47) passing through a given point {x, y) in a given direction y', is found by eliminating y" between 4(l + y^V 6(1 + y-^)'^ ^2 = 2y^' '^^ — ^^'^y + ^2;» (1 + y"), .
What to read after Geometric Properties Completely Characterizing All the Curves in a Plane Along W?
You can find similar books in the "Read Also" column, or choose other free books by Sarah Elizabeth Cronin to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Substituting the values from (45) in (46), we obtain Solving this for B2, making a slight change in notation, we obtain B2 = Hiy"-{-H2, where Hi and H2 are arbitrary functions of x, y, 3^.
All the quadruply infinite systems having properties I, II, III are then defined by the differential equation 2/"^ = ^ y'"^ + ili^y" + H2)y'" + Bz, (47) where Hi and H2 are arbitrary functions of x, y, y' and B% is an arbitrary function of x, y, y', y" .
Section 4- Conversion of Property IV. In order to conve...rt Theorem IV, we state it in a form which does not assume the existence of a force, as follows: At each point {x, y) of the plane, there exists a certain direction of slope co(x, y) svxih that the sine of twice the angle this direction makes with the given element is equal to three times the tangent of the angle the given element makes with the parabola corresponding to it by theorem III.
CONVERSION OF PROPERTIES. 17 The parabola corresponding, in accordance with property III, to the 00 2 curves of system (47) passing through a given point {x, y) in a given direction y', is found by eliminating y" between 4(l + y^V 6(1 + y-^)'^ ^2 = 2y^' '^^ — ^^'^y + ^2;» (1 + y"), .
What to read after Geometric Properties Completely Characterizing All the Curves in a Plane Along W?
You can find similar books in the "Read Also" column, or choose other free books by Sarah Elizabeth Cronin to read onlineMoreLess
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