An explicit formula for spherical curves with constant torsion
نویسندگان
چکیده
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 کاملSpherical Bessel functions and explicit quadrature formula
An evaluation of the derivative of spherical Bessel functions of order n + 1 2 at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.
متن کاملLength Minimization for Space Curves Undernonholonomic Constraints : the Constant Torsion
The Griiths formalism is applied to nd constant torsion curves which are extremal for arclength with respect to variations preserving torsion, xing 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 nd the...
متن کاملTopology and Sine-gordon Evolution of Constant Torsion Curves
The sine-Gordon equation with periodic boundary conditions describes integrable dynamics on the space of closed curves of constant torsion, for which multi-phase solutions provide large classes of canonical knot representatives. In this letter we discuss the use of Bäcklund transformations for studying the topological properties and symmetries of multi-phase solutions and of their homoclinic ma...
متن کاملAn explicit formula for the matrix logarithm
We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment {I(1 − t) + At : t ∈ [0, 1]} joining the identity matrix I (at t = 0) to any real matrix A (at t = 1) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer’s method for evaluating the matrix exponential. Key-words...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2012
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2012.259.361