THE CATENARY IN SPACE. FREE MOTIONS OF FLEXIBLE LINES.

Abstract

The nature and importance of the catenary in space (flexible systems in one dimension) are discussed. Equations of motion are developed in more complete and universal form than in the literature. The catenary is described by means of a system of four, first-order, quasilinear, hyperbolic, partial differential equations. The special circumstances are treated where the first order system reduces to a standard second order wave equation familiar in the literature. The four characteristics of the hyperbolic system are found and also the vectors which help formulate combination variables suitable for the catenary problem. Some special solutions are presented for interesting catenary motions. A general treatment is formulated in terms of integral equations for the full catenary problem of planar motion with two independent variables and four dependent catenary parameters. Extensions to other novel problems are indicated. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0611429

Entities

People

  • R. M. Langer

Tags

DTIC Thesaurus Topics

  • Catenaries
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Integral Equations
  • Integrals
  • Literature
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Electrical Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design

Technology Areas

  • Space