Intrinsic equations for a relaxed elastic line on an oriented surface

✍ Scribed by H. K. Nickerson; Gerald S. Manning

• Book ID: 104643828
• Publisher: Springer
• Year: 1988
• Tongue: English
• Weight: 342 KB
• Volume: 27
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00151344

✦ Synopsis

p. 221]

incorrectly suggested a flexible knitting needle, constrained to conform to a surface, as one model for a geodesic on a surface. This model actually gives a relaxed elastic line on the surface, and is not generally a geodesic unless the surface lies in a plane or on a sphere.

In this paper we derive the intrinsic equations for a relaxed elastic line on an oriented surface. This formulation should give a more direct and more geometric approach to questions concerning relaxed elastic lines on a surface. We apply this formulation to give alternate proofs of some results of [3] found by the less direct method of Lagrange multipliers and to give additional results about relaxed elastic lines on various surfaces. For further considerations of a relaxed elastic line on a surface as a model of the DNA molecule, see [3].

1. DERIVATION OF EQUATIONS n ~ _ K n --T O

• Partially supported by NIH grant GM 36284-01.