Browsing Department of Mathematics and Statistics: Dr. Andrew D. Lewis by Title
Now showing items 17-33 of 33
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High-order variations for families of vector fields
(2002)Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order ... -
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. -
Low-order 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, low-order 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)Time-optimal and force-optimal 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 observer-independent 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 Euler-Lagrange equations in a ``force balance'' form. The key ingredient in such a construction is the Euler-Lagrange 2-force 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 ...