Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations

Hamiltonian dynamics of planar affinely-rigid body

The general formulation of the mechanics of an affinely-rigid body in n dimensions was presented in [1, 2, 3]. Obviously, it is the special case n = 3 that is directly physically applicable, if a proper potential model is chosen. For realistic potentials, the three-dimensional problem is very difficult. The reason is that the group SO(3, IR) (and generally SO(n, IR) for n > 2) is semisimple and...

Dynamics and Controllability of a Planar Rigid Body with aThruster

In this paper we discuss the dynamics of a planar rigid body with a thruster. We identify the position and orientation of the planar rigid body with an element of the Lie group SE(2). The invariance of the kinetic energy Lagrangian and the forcing term (thrust) under the SE(2) action of translations and rotations is used to obtain a set of Poisson-reduced equations on T SE(2)=SE(2) which is iso...

On the Large Angle Problem in Rigid Body Attitude Dynamics

For many problems involving rotating rigid bodies (e.g. spin-stabilized satellites in space) one usually linearizes the equations of motion for the Eulerian angles to obtairi tractable analytic solutions. However, these methods -based on a small angle assumption have failed to provide a comprehensive treatment of the behavior of a rigid body during large angular motioris that occur, for example...

Fast Simulations of Gravitational Many-body Problem on RV770 GPU

The gravitational many-body problem is a problem concerning the movement of bodies, which are interacting through gravity. However, solving the gravitational many-body problem with a CPU takes a lot of time due to O(N) computational complexity. In this paper, we show how to speed-up the gravitational many-body problem by using GPU. After extensive optimizations, the peak performance obtained so...

Title : Rigid body dynamics