A Treatise On the Differential Geometry of Curves And Surfaces
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In deriving them we refer the surface to a moving set of rectangular axes called the trihedral T. Its ver- tex M is a point of the surface, the zy-plane is tangent to the surface at M, and the positive 2-axis coincides with the positive direction of the normal to the surface at M. The position of the x- and y-axes is determined by the angle U which the tangent to the curve v = const, through M makes with the a^axis, U being a given function of u and v.
In Chapter I we considered another moving ...trihedral, consisting of the tangent, principal normal, and binormal of a twisted curve.
Let us associate such a trihedral with the curve v = const, through THE MOVING TEIHEDEAL 16T M and call it the trihedral t u . We have found (§ 16) that the varia- tions of the direction-cosines a', b', c' of a line L, fixed in space, with reference to t u , as its vertex moves along the curve which we call C u , are given by ds u P J d* u \ Pa tJ ds~ t„' where p u , r u denote the radii of first and second curvature of C u , and ds u its linear element ; evidently the latter may be replaced by VlUdu.
What to read after A Treatise On the Differential Geometry of Curves And Surfaces?
You can find similar books in the "Read Also" column, or choose other free books by Luther Pfahler Eisenhart to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In deriving them we refer the surface to a moving set of rectangular axes called the trihedral T. Its ver- tex M is a point of the surface, the zy-plane is tangent to the surface at M, and the positive 2-axis coincides with the positive direction of the normal to the surface at M. The position of the x- and y-axes is determined by the angle U which the tangent to the curve v = const, through M makes with the a^axis, U being a given function of u and v.
In Chapter I we considered another moving ...trihedral, consisting of the tangent, principal normal, and binormal of a twisted curve.
Let us associate such a trihedral with the curve v = const, through THE MOVING TEIHEDEAL 16T M and call it the trihedral t u . We have found (§ 16) that the varia- tions of the direction-cosines a', b', c' of a line L, fixed in space, with reference to t u , as its vertex moves along the curve which we call C u , are given by ds u P J d* u \ Pa tJ ds~ t„' where p u , r u denote the radii of first and second curvature of C u , and ds u its linear element ; evidently the latter may be replaced by VlUdu.
What to read after A Treatise On the Differential Geometry of Curves And Surfaces?
You can find similar books in the "Read Also" column, or choose other free books by Luther Pfahler Eisenhart to read onlineMoreLess
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