Browsing Department of Mathematics and Statistics: Dr. Andrew D. Lewis by Title
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Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
(2004)Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability ... 
Rigid body mechanics in Galilean spacetimes
(2004)An observerindependent formulation of rigid body dynamics is provided in the general setting of a Galilean spacetime. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime ... 
Simple mechanical control systems with constraints
(IEEE, 2000)We apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints. Certain simple aspects of the theory of affine connections play an important part in our ... 
Towards F=ma in a general setting for Lagrangian mechanics
(1998)By using a suitably general definition of a force, one may geometrically cast the EulerLagrange equations in a ``force balance'' form. The key ingredient in such a construction is the EulerLagrange 2force which is a ... 
Variational principles for constrained systems: theory and experiment
(1994)In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also ...