Advertisement

N-Body Systems*

  • Kenneth Eriksson
  • Donald Estep
  • Claes Johnson
Chapter

Abstract

We shall now model systems of N bodies interacting through mechanical forces that result from springs and dashpots, see Fig. 48.1, or from gravitational or electrostatic forces. We shall use two different modes of description. In the first formulation, we describe the system through the coordinates of (the centers of gravity of) the bodies. In the second, we use the displacements of the bodies measured from an initial reference configuration. In the latter case, we also linearize under an assumption of small displacements to obtain a linear system of equations. In the first formulation, the initial configuration is only used to initialize the system and is “forgotten” at a later time in the sense that the description of the system only contains the present position of the masses. In the second formulation, the reference configuration is retrievable through the evolution since the unknown is the displacement from the reference position. The different formulations have different advantages and ranges of application.

Keywords

Electrostatic Force Gravitational Force Small Displacement Reference Position Reference Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kenneth Eriksson
    • 1
  • Donald Estep
    • 2
  • Claes Johnson
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.Department of MathematicsColorado State UniversityFort CollinsUSA

Personalised recommendations