DIFFERENTIAL EQUATIONS WITH A DISCONTINUOUS FORCING TERM

Abstract

A solution is given for the problem of finding a transition or switching curve in the phase plane for the expression mx + cx + kx = Df(x,x) so that solutions reach the zero state in a minimum time. The solution has applications in the design of servomechanisms and similar systems; f is a discontinuous function which assumes only + of - 1. The solution required the problem to be broken up into cases. Curves are included showing points in the xx phase plane at which f switches from +1 to -1 and vice versa.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1953
Accession Number
AD0002209

Entities

People

  • Donald W. Bushaw

Organizations

  • Stevens Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Control Systems
  • Coordinate Systems
  • Crossings
  • Differential Equations
  • Equations
  • Frequency
  • Geometric Forms
  • Geometry
  • Inequalities
  • Lines (Geometry)
  • Mathematics
  • Military Research
  • Quadrants
  • Regions
  • Sequences
  • Theses
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra