Lie-Poisson integration for rigid body dynamics

Lie Group Formulation of Articulated Rigid Body Dynamics

It has been usual in most old-style text books for dynamics to treat the formulas describing linear(or translational) and angular(or rotational) motion of a rigid body separately. For example, the famous Newton’s 2nd law, f = ma, for the translational motion of a rigid body has its partner, so-called the Euler’s equation which describes the rotational motion of the body. Separating translation ...

Efficient Lie-Poisson Integrator for Secular Spin Dynamics of Rigid Bodies

A fast and efficient numerical integration algorithm is presented for the problem of the secular evolution of the spin axis. Under the assumption that a celestial body rotates around its maximum moment of inertia, the equations of motion are reduced to the Hamiltonian form with a Lie-Poisson bracket. The integration method is based on the splitting of the Hamiltonian function and so it conserve...

Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body.

The classical Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point are generalized to arbitrary Lie algebras as Hamiltonian systems on coad-joint orbits of a tangent bundle Lie group. the N-dimensional Lagrange and symmetric heavy top are thereby shown to be completely integrable.

Title : Rigid body dynamics

3D Rigid Body Dynamics

The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Euler angles: spin ψ̇, nutation θ and precession φ shown below in Figure 1. In this case we surmount the difficulty of keeping track of the principal axes fixed to the body by making their orientation the unknowns in our equations of motion; then the angular velocities and angula...