©
Catenary with concentrated loads
  Computes a catenary, as an inextensible cable, with concentrated loads, via shooting.
2024.May.10 18:37:34
xB, yB   (Point A is the origin.) Coordinates of point B (non-dimensional).† •
θ,  q ([θ] = °)   Initial (at A) θ and q (according to 'Mode'‡). •
nconc (Must match foll. !) No. of concentrated loads. •
Loads Position, loadx, loady. •
h Integration step.
scale, tol   (NM = Nelder-Mead) NM: scale for variables; tolerance. •
Mode   Mode: solve or audit (explore). •
itmax, iprt NM: max. iterations; intermediate test. •
Graph   Graph to make. •
Show values ? Shows the graph coordinates.

Warning: Pls., afterwards see the graph here (check the date).

Computes the behaviour of a catenary, as an inextensible cable, via the Nelder-Mead (NM) algorithm. For details, see the plate by Newton-Raphson. The method solves the original nconc ODE's.

† The coordinates of B must lie in a unit circle, and the tension, q, is given as related to the cable weight (due to the non-dimensional formulation).

‡ Mode: in solve mode, resolution is attempted from mid-θ and mid-q; in audit mode, an exploration is made in those ranges (the "surface", however, is not shown here).

The graph shows: (a) y (catenary) vs. x; or (b) θ (green) and q (red) vs. s.

Other proposed data: (.35, .35; 65, .005).

Problem: suggested and managed by Prof. A. Pinto da Costa, IST.

References: Plate: CatenaryLoads

• 1713-05-07: Clairaut, Alexis Claude (1765-05-17).

 
 
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Created: 2010-05-07 — Last modified: 2024-01-02