We consider the mathematical model of a rigid ball moving in a viscous incompressible fluid occupying a bounded domain Ω, with an external force acting on the ball. We investigate in particular the case when the external force is what would be produced by a spring and a damper connecting the center of the ball h to a fixed point h1 ∈ Ω. If the initial fluid velocity is sufficiently small, and t...

Visual servo controllers in the literature rarely achieve provably large domains of attraction, and seldom address two important sensor limitations: (i) susceptibility to self-occlusions and (ii) finite field of view (FOV). In this paper, we tackle the problem of global, occlusion-free visual servoing of a fully actuated rigid body by recourse to navigation functions on a compact manifold which...

Geometric algebra is used in an essential way to provide a coordinatefree approach to Euclidean geometry and rigid body mechanics that fully integrates rotational and translational dynamics. Euclidean points are given a homogeneous representation that avoids designating one of them as an origin of coordinates and enables direct computation of geometric relations. Finite displacements of rigid b...

In this paper, we present an algorithm to propagate an n-ary constraint (with n greater than 2) specifying the relative positions of points in a three-dimensional rigid group. The variables to restrict are the positions (x, y, and z coordinates) of the points, and we assume the variable domains are cuboids, with the faces parallel to the coordinate axes. This algorithm is part of PSICO (Process...

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying...

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.

The integrability theory for the differential equations, which describe the motion of an unconstrained rigid body around a fixed point is well known. When there are constraints the theory of integrability is incomplete. The main objective of this paper is to analyze the integrability of the equations of motion of a constrained rigid body around a fixed point in a force field with potential U(γ ...

Please note: This document is ©2001 by David Baraff. This chapter may be freely duplicated and distributed so long as no consideration is received in return, and this copyright notice remains intact.

This paper explains the relationship between two existing representations of rigid-body acceleration in a 6-D vector: conventional acceleration, which is the concatenation of two 3-D acceleration vectors, and spatial acceleration, which is the time derivative of a 6-D velocity vector. The two are materially different and obey different composition rules. In particular, spatial accelerations beh...

In this paper we analyze an alternative formulation of the rigid body equations, their relationship with the discrete rigid body equations of Moser–Veselov and their formulation as an optimal control problem. In addition we discuss a general class of discrete optimal control problems.