Complementary Curves of Descent

Abstract

The shapes of two wires in a vertical plane with the same starting and ending points are described as complementary curves of descent if beads frictionlessly slide down both of them in the same time, starting from rest. Every analytic curve has a unique complement, except for a cycloid (solution of the brachistochrone problem), which is self complementary. A striking example is a straight wire whose complement is a lemniscate of Bernoulli. Alternatively the wires can be tracks down which round objects undergo a rolling race. The level of presentation is appropriate for an intermediate undergraduate course in classical mechanics.

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Document Details

Document Type
Technical Report
Publication Date
Nov 16, 2012
Accession Number
ADA577522

Entities

People

  • Carl E. Mungan
  • Trevor C. Lipscombe

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Cartesian Coordinates
  • Electronic Mail
  • Energy
  • Equations
  • Kinetic Energy
  • Mathematics
  • Mechanical Energy
  • Mechanics
  • Moment Of Inertia
  • Physics
  • Quadrants
  • Students
  • Two Dimensional
  • United States Naval Academy
  • Vertical Orientation

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research
  • Structural Dynamics.