Orbits on a Concave Frictionless Surface

Abstract

The equations of motion of a puck sliding frictionlessly inside a parabolic bowl can be straightforwardly deduced using the conservation laws of mechanical energy and angular momentum. But the solution of these equations requires that they be recast into the form of Newton's second law. The simple example of a ball in vertical freefall illustrates why this is necessary and how to perform the conversion. The method is then applied to the richer problem of a puck gliding on a paraboloidal surface for which the nonlinear equations require numerical solution. A rich variety of orbital patterns of the puck is found.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA574905

Entities

People

  • Carl E. Mungan
  • Sean A. Genis

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Abstracts
  • Air Resistance
  • Angular Momentum
  • Centrifugal Force
  • Circular Orbits
  • Computer Programs
  • Coordinate Systems
  • Differential Equations
  • Energy
  • Equations
  • Gravitational Fields
  • Instructors
  • Numbers
  • Orbits
  • Square Roots
  • Trajectories
  • United States Naval Academy

Fields of Study

  • Mathematics
  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Tribology (the study of the boundary interaction between sliding surfaces, lubrication, wear and friction).

Technology Areas

  • Space
  • Space - Orbital Debris
  • Space - Spacecraft Maneuvers