Two connected bodies in a central gravitational field

Amit Sanyal, Anthony Bloch

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

The dynamics of two bodies connected by a hinge joint, and moving in a plane under the action of a central gravitational force field is analyzed. Each body is modeled as a rigid massless link with a point mass at one end; their other ends are connected together by a hinge joint The equations of motion of the connected bodies include the equations for the orbital motion of the bodies, the orientation (attitude) of the assembly, and the relative orientation (shape) of the bodies with respect to each other. Dynamic coupling between these degrees of freedom give rise to a complex dynamical system. Relative equilibria, corresponding to circular orbits of fixed radius, are obtained from these equations of motion. The free dynamics has a symmetry due to the cyclic coordinate representing the true anomaly. Routh reduction is carried out to eliminate this coordinate and obtain the reduced dynamics. We carry out stability analysis for the relative equilibria. Numerical simulations using a symplectic integrator are carried out for perturbations from these relative equilibria, to confirm their stability properties. These numerical simulations also suggest the use of shape change to alter the overall orientation and orbit of the assembly.

Original languageEnglish (US)
Article numberThC09.5
Pages (from-to)3968-3973
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
StatePublished - Dec 1 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

Fingerprint

Gravitational Field
Relative Equilibria
Hinges
Equations of motion
Equations of Motion
Orbits
Orbit
Symplectic Integrators
Complex Dynamical Systems
Numerical Simulation
Computer simulation
Degrees of freedom (mechanics)
Force Field
Anomaly
Stability Analysis
Dynamical systems
Eliminate
Degree of freedom
Radius
Perturbation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Two connected bodies in a central gravitational field. / Sanyal, Amit; Bloch, Anthony.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 4, ThC09.5, 01.12.2004, p. 3968-3973.

Research output: Contribution to journalConference article

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