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Lie group variational integrators for the full body problem

โœ Scribed by Taeyoung Lee; Melvin Leok; N. Harris McClamroch

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
739 KB
Volume
196
Category
Article
ISSN
0045-7825

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โœฆ Synopsis

We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of rigid body configurations. Both continuous equations of motion and variational integrators are developed in Lagrangian and Hamiltonian forms, and the reduction from the inertial frame to a relative frame is also carried out. The Lie group variational integrators are shown to be symplectic, to preserve conserved quantities, and to guarantee exact evolution on the configuration space. One of these variational integrators is used to simulate the dynamics of two rigid dumbbell bodies.

๐Ÿ“œ SIMILAR VOLUMES

Lie group methods for rigid body dynamic
Lie group methods for rigid body dynamics and time integration on manifolds
โœ Elena Celledoni; Brynjulf Owren ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 496 KB

Recently there has been an increasing interest in time integrators for ordinary differential equations which use Lie group actions as a primitive in the design of the methods. These methods are usually phrased in an abstract sense for arbitrary Lie groups and actions. We show here how the methods lo