Browsing Department of Mathematics and Statistics: Dr. Andrew D. Lewis by Title
Now showing items 1833 of 33

Jacobian linearisation in a geometric setting
(IEEE, 2003)Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential ... 
Kinematic controllability and motion planning for the snakeboard
(IEEE, 2003)The snakeboard is shown to be kinematically controllable. Associated with the two decoupling vector fields for the problem, a constrained static nonlinear programming problem is posed whose solutions provide a solution to ... 
Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
(D. Reidel, 1992)In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple ... 
Lifting distributions to tangent and jet bundles
(1998)We provide two natural ways to lift a distribution from a manifold to its tangent bundle, and show that they agree if and only if the original distribution is integrable. The case when the manifold is the total space ... 
The linearisation of a simple mechanical control system
(2002)A geometric interpretation is given for the linearisation of a mechanical control system with a kinetic minus potential energy Lagrangian. 
Loworder controllability and kinematic reductions for affine connection control systems
(2002)Controllability and kinematic modeling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for a class of mechanical control systems. Second, a ... 
Nonholonomic mechanics and locomotion: the snakeboard example
(IEEE, 1994)Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard.1 Although the model exhibits basic gait patterns seen in a large number of ... 
On the homogeneity of the affine connection model for mechanical control systems
(IEEE, 2000)This work presents a review of a number of control results for mechanical systems. The key technical results derive mainly from the homogeneity properties of affine connection models for a large class of mechanical systems. ... 
Optimal control for a simplified hovercraft model
(2000)Timeoptimal and forceoptimal extremals are investigated for a planar rigid body with a single variable direction thruster. A complete and explicit characterisation of the singular extremals is possible for this problem. 
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 ...