Hamiltonian dynamics of planar affinely-rigid body

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...

Quantization of the planar affinely-rigid body

This paper is a continuation of [1] where the classical model was analyzed. Discussed are some quantization problems of two-dimensional affinely rigid body with the double dynamical isotropy. Considered are highly symmetric models for which the variables can be separated. Some explicit solutions are found using the Sommerfeld polynomial method.

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...

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...