Finding Stable Orientations of Assemblies with Linear Programming

Abstract

In the paper by Mattikalli et al.(5), the stability of an assemblage of frictionless contacting bodies with uniform gravity was considered. The problem of finding a stable orientation for such an assembly was formulated as a constrained maximum problem. A solution to the maximum problem yielded an orientation of the assembly that was stable under gravity; however, if no such orientation existed, then the solution to the maximum problem yielded the most stable orientation possible for the assembly. The maximum problem was solved using a numerical iteration procedure that solved a linear program for each step of the iteration. In this paper, we show that the stability problem can be considered a variant of standard zero-sum matrix games. A solution to the maximum problem can be found by solving a single linear program.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1993
Accession Number
ADA266990

Entities

People

  • Bruno Repetto
  • David Baraff
  • Pradeep Khosla
  • Raju Mattikalli

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Assembly
  • Computer Programming
  • Displacement
  • Energy
  • Equations
  • Inequalities
  • Kinetic Energy
  • Linear Programming
  • Linear Systems
  • Matrix Games
  • Orientation (Direction)
  • Particles
  • Potential Energy
  • Recreation
  • Relative Motion
  • Zero-Sum Games

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Operations Research