منابع مشابه
Minimal Curves of Constant Torsion
The Griffiths formalism is applied to find constant torsion curves which are extremal for arclength with respect to variations preserving torsion, fixing the endpoints and the binormals at the endpoints. The critical curves are elastic rods of constant torsion, which are shown to not realize certain boundary conditions. In the calculus of variations under nonholonomic constraints, one tries to ...
متن کاملCurves with Constant Curvature Ratios
The notion of a generalized helix in R3, a curve making a constant angle with a fixed direction, can be generalized to higher dimensions in many ways. In [7] the same definition is proposed but in R. In [4] the definition is more restrictive: the fixed direction makes a constant angle with all the vectors of the Frenet frame. It is easy to check that this definition only works in the odd dimens...
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In the euclidean plane, a regular curve can be defined through its intrinsic equation which relates its curvature k to the arc length s. Elastic plane curves were determined this way. If k(s) = 2α cosh(αs) , the curve is known by the name “la courbe des forçats”, introduced in 1729 by Giovanni Poleni in relation with the tractrix [9]. The above equation is yet meaningful on a surface if one int...
متن کاملCurves of constant diameter and inscribed polygons
If one drops the unicity assumption, (C(D)) is the property of having constant diameter, which is in fact equivalent (for closed curves in the plane) to having constant width or constant breadth (for the definitions and the proof of the equivalence, see [8, chap. 25]). It is a surprise to many (including me !) that curves of constant diameter other that the circle do exist. The simplest example...
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The Study of heat transfer augmentation in micro scale and electronic packaging systems are some of the paramount areas of the impending universe. In such systems the cooling of the heat sinks are generally achieved through the impingement of air jet. Assuming the air jet to be continues & incompressible fluid, the heat dissipation rate over the target surface seems to either uniform or well ch...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1973
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1973.101148