Tiltup Panels: Locate the Pulleys (UMAP)

This module discusses the location of the pulleys for a cable rigging currently in use. The key differenetial equation is based on an explicit expression for the distance of a point from an ellipse. The Lagrange multiplier of the corresponding optimization problem appears explicitly in this expression and is computed numerically by Newton's method. The appearance of the Lagrange multiplier in the expression for the distance of a point from an ellipse and in the key differential equation is somewhat unusual.

Table of Contents:

1. INTRODUCTION

2. THE MODEL

3. LAGRANGE MULTIPLIERS AND THE DISTANCE OF A POINT FROM A CURVE

4. VECTORS

5. NEWTON'S METHOD

6. THE DISTANCE OF A POINT FROM AN ELLIPSE

7. THE KEY DIFFERENTIAL EQUATION

8. REFERENCES

9. SOLUTIONS

APPENDIX 1: PROGRAM THAT COMPUTES THE DISTANCE BETWEEN A POINT AND AN ELLIPSE