Dynamics of multibody systems in planar motion in a central gravitational field

Amit Sanyal, Anthony Bloch, N. Harris Mcclamroch

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Multibody systems in planar motion are modelled as two or more rigid components that are connected and can move relative to each other. The dynamics of such multibody systems in planar motion in a central gravitational force field is analysed. The equations of motion of the system 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 gives rise to complex dynamical systems that are usually not integrable. Relative equilibria, corresponding to circular orbits of the multibody system, are obtained. The free dynamics has a symmetry due to a cyclic coordinate. Routh reduction is carried out to eliminate this coordinate and obtain the reduced dynamics. The stability of the relative equilibria is analysed using the Routh stability criterion when it is applicable; an expansion of the Hamiltonian in normal form is used otherwise. We apply the general results to a multibody system consisting of two hinged planar bodies, each modelled as a rigid massless link with a point mass at one end with their other ends connected by a hinge joint. We obtain the relative equilibria of this model, and carry out a stability analysis for the relative equilibria. Numerical simulations using a symplectic integrator are carried out fer perturbations to these relative equilibria, to confirm their stability properties.

Original languageEnglish (US)
Pages (from-to)303-343
Number of pages41
JournalDynamical Systems
Volume19
Issue number4
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

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Relative Equilibria
Multibody Systems
Gravitational Field
Motion
Hamiltonians
Symplectic Integrators
Complex Dynamical Systems
Degrees of freedom (mechanics)
Stability criteria
Hinges
Equations of motion
Force Field
Dynamical systems
Orbits
Stability Criteria
Normal Form
Stability Analysis
Equations of Motion
Eliminate
Orbit

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Cite this

Dynamics of multibody systems in planar motion in a central gravitational field. / Sanyal, Amit; Bloch, Anthony; Mcclamroch, N. Harris.

In: Dynamical Systems, Vol. 19, No. 4, 01.12.2004, p. 303-343.

Research output: Contribution to journalArticle

Sanyal, Amit ; Bloch, Anthony ; Mcclamroch, N. Harris. / Dynamics of multibody systems in planar motion in a central gravitational field. In: Dynamical Systems. 2004 ; Vol. 19, No. 4. pp. 303-343.
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