Andrew D. Lewis's Preprints


I do not mind if you think slowly, but I do object when you publish more quickly than you think — Wolfgang Pauli


The listing is roughly in reverse chronological order. The "Last Updated" tag means the last time the pdf files were updated, not the TeX files.

For papers where published versions are available, I have included a link to these. Most require some sort of subscription. If you click on the title, you get the abstract and my personal version of the paper, which will differ somewhat from the published version.

Here is the AMS Subject Classification.

2023a
Title: Geometric and function analytic methods for flows of time- and parameter-dependent vector fields
Author(s): Andrew D. Lewis
Detail: Preprint

2022a
Title: The exponential map for time-varying vector fields
Author(s): Yanlei Zhang
Detail: PhD Thesis, Queen's University

2021a
Title: Integrable and absolutely continuous vector-valued functions
Author(s): Andrew D. Lewis
Detail: Rocky Mountain Journal of Mathematics, 52(3), pages 925-947, 2022
Journal version: Download

2020b
Title: Gelfand duality for manifolds, and vector and other bundles
Author(s): Andrew D. Lewis
Detail: Differential Geometry and its Applications, 91 102050, 2023
Journal version: Download

2020a
Title: Identifying physical trajectories of nonholonomic mechanical systems as constrained variational trajectories
Author(s): Ahmed G. Shaltut
Detail: MSc Thesis, Queen's University

2019b
Title: Control of nonholonomic mechanical systems using virtual surfaces
Author(s): Scott M. Kyle
Detail: MSc Thesis, Queen's University

2019a
Title: Nonholonomic and constrained variational methods applied to a rolling disc
Author(s): Julian Christopher
Detail: MSc Thesis, Queen's University

2018a
Title: Nonholonomic and constrained variational mechanics
Author(s): Andrew D. Lewis
Detail: Journal of Geometric Mechanics, 12(2), pages 165-308, 2020
Journal version: Download

2017a
Title: The bountiful intersection of differential geometry, geometric mechanics, and geometric control theory
Author(s): Andrew D. Lewis
Detail: Annual Review of Control, Robotics, and Autonomous Systems, 1, 1.135-1.158, 2018
Journal version: Download

2016c
Title: Degeneracy of velocity constraints in rigid body systems
Author(s): Jonny Briggs
Detail: MSc Thesis, Queen's University

2016b
Title: Remarks on stability of time-varying linear systems
Author(s): Andrew D. Lewis
Detail: IEEE Transactions on Automatic Control, 62(11), 6039-6043, 2017
Journal version: Download

2016a
Title: On the role of regularity in mathematical control theory
Author(s): Saber Jafarpour
Detail: PhD Thesis, Queen's University

2015a
Title: Linearization and stability of nonholonomic mechanical systems
Author(s): Steven D. Yang
Detail: MSc Thesis, Queen's University

2014g
Title: The physical foundations of geometric mechanics
Author(s): Andrew D. Lewis
Detail: Journal of Geometric Mechanics, 9(4), 487-574, 2017
Journal version: Download

2014f
Title: Real analytic control systems
Author(s): Saber Jafarpour and Andrew D. Lewis
Detail: Proceedings of the 53rd IEEE Conference on Decision and Control, December 2014, pages 5618-5623
Conference proceedings version: Download

2014e
Title: Tautological control systems
Author(s): Andrew D. Lewis
Detail: Proceedings of the 53rd IEEE Conference on Decision and Control, December 2014, pages 4832-4837
Conference proceedings version: Download

2014d
Title: Linearisation of tautological control systems
Author(s): Andrew D. Lewis
Detail: Journal of Geometric Mechanics, 8(1), pages 99-138, 2016
Journal version: Download

2014c
Title: Tautological control systems
Author(s): Andrew D. Lewis
Detail: Springer Briefs in Electrical and Computer Engineering - Control, Automation and Robotics, Springer-Verlag, 2014, ISBN 978-3-319-08638-5 (The online version I have not as complete as the Springer version.)
Journal version: Download

2014b
Title: Locally convex topologies and control theory
Author(s): Saber Jafarpour and Andrew D. Lewis
Detail: Mathematics of Control, Signals and Systems 28(4), pages 1-46, 2016
Journal version: Download

2014a
Title: Time-varying vector fields and their flows
Author(s): Saber Jafarpour and Andrew D. Lewis
Detail: Springer Briefs in Mathematics, Springer-Verlag, 2014, ISBN 978-3-319-10139-2
Journal version: Download

2013b
Title: Some observations on orbits of driftless bilinear systems
Author(s): Melkior Ornik
Detail: MSc Thesis, Queen's University

2013a
Title: Mathematical models for geometric control theory
Author(s): Saber Jafarpour and Andrew D. Lewis
Detail: Preprint
This gigantic paper will be broken into smaller pieces, namely one about locally convex topologies and time varying vector fields, one about locally convex topologies and control theory, one about so-called "tautological control systems," and one about linearisation of tautological control systems.

2012b
Title: Feedback stabilisation of locally controllable systems
Author(s): Pantelis Isaiah
Detail: PhD Thesis, Queen's University

2012a
Title: Fundamental problems of geometric control theory
Author(s): Andrew D. Lewis
Detail: Proceedings of 51st IEEE Conference on Decision and Control, December 2012, pages 7511-7516
Conference proceedings version: Download

2011b
Title: Small-time local controllability of homogeneous systems
Author(s): César O. Aguilar and Andrew D. Lewis
Detail: SIAM Journal on Control and Optimization 50(3), pages 1502-1517, 2012
Journal version: Download

2011a
Title: Geometric interpretations of the symmetric product in affine differential geometry
Author(s): María Barbero-Liñán and Andrew D. Lewis
Detail: International Journal of Geometric Methods in Modern Physics, 9(8), 1250073, 2012
Journal version: Download

2010b
Title: Geometric Jacobian linearization and LQR theory
Author(s): Andrew D. Lewis and David R. Tyner
Detail: Journal of Geometric Mechanics, 2(4), pages 397-440, 2010
Journal version: Download

2010a
Title: Local controllability of affine distributions
Author(s): César O. Aguilar
Detail: PhD Thesis, Queen's University

2009a
Title: A geometric approach to energy shaping
Author(s): Bahman Gharesifard
Detail: PhD Thesis, Queen's University

2008b
Title: A geometric framework for stabilization by energy shaping: Sufficient conditions for existence of solutions
Author(s): Bahman Gharesifard, Andrew D. Lewis, and Abdol-Reza Mansouri
Detail: Communications for Information and Systems 8(4), Special issues dedicated to Roger Brockett, pages 353-398, 2008
Journal version: Download

2008a
Title: Jet bundles and algebro-geometric characterisations for controllability of affine systems
Author(s): César O. Aguilar and Andrew D. Lewis
Detail: Proceedings of the 47th IEEE Conference on Decision and Control, December 2008, pages 1267-1274
Conference proceedings version: Download

2007b
Title: Geometric Jacobian linearization
Author(s): David R. Tyner
Detail: PhD Thesis, Queen's University

2007a
Title: Geodesic reduction via frame bundle geometry
Author(s): Ajit Bhand
Detail: PhD Thesis, Queen's University

2006b
Title: Is it worth learning differential geometric methods for modelling and control of mechanical systems?
Author(s): Andrew D. Lewis
Detail: Robotica 26(6), pages 765-777, November 2007
Journal version: Download

2006a
Title: Potential energy shaping after kinetic energy shaping
Author(s): Andrew D. Lewis
Detail: Proceedings of the 45th IEEE Conference on Decision and Control, December 2006, pages 3339-3344
Conference proceedings version: Download

2005b
Title: An example with interesting controllability and stabilisation properties
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: Proceedings of the 45th IEEE Conference on Decision and Control, December 2006, pages 3748-3753
Conference proceedings version: Download

2005a
Title: Coordinate-free derivation of the Euler-Lagrange equations and identification of global solutions via local behavior
Author(s): Elsa K. Hansen
Detail: MSc Thesis, Queen's University

2004d
Title: Notes on energy shaping
Author(s): Andrew D. Lewis
Detail: Proceedings of the 43rd IEEE Conference on Decision and Control, December 2004, pages 4818-4823
Conference proceedings version: Download

2004c
Title: Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: Acta Applicandae Mathematicae, 99(1), pages 53-95, 2007
Journal version: Download

2004b
Title: Discussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
Author(s): Andrew D. Lewis
Detail: European Journal of Control, 11, 12-15, 2005
Journal version: Download

2004a
Title: Rigid body mechanics in Galilean spacetimes
Author(s): Ajit Bhand and Andrew D. Lewis
Detail: Journal of Mathematical Physics, 46(11), 102902, 29 pages, 2005
Journal version: Download

2003c
Title: Geometric sliding mode control: the linear and linearized theory
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: Proceedings of the 42nd IEEE Conference on Decision and Control, December 2003, pages 2971-2976
Conference proceedings version: Download

2003b
Title: Controllability of a hovercraft model (and two general results)
Author(s): Andrew D. Lewis and David R. Tyner
Detail: Proceedings of the 43rd IEEE Conference on Decision and Control, December 2004, pages 1204-1209
Conference proceedings version: Download

2003a
Title: Jacobian linearisation in a geometric setting
Author(s): Andrew D. Lewis and David R. Tyner
Detail: Proceedings of the 42nd IEEE Conference on Decision and Control, December 2003, pages 6084-6089
Conference proceedings version: Download

2002g
Title: Linearization of affine connection control systems
Author(s): David Tyner
Detail: MSc Thesis, Queen's University

2002f
Title: Rigid body mechanics in Galilean spacetimes
Author(s): Ajit Bhand
Detail: MSc Thesis, Queen's University

2002e
Title: Low-order controllability and kinematic reductions for affine connection control systems
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: SIAM Journal on Control and Optimization 44(3), pages 885-908, 2005
Journal version: Download

2002d
Title: What is the characteristic polynomial of a signal flow graph?
Author(s): Andrew D. Lewis
Detail: Sixty Open Problems in Mathematical Systems and Control Theory, Vincent Blondel and Alexandre Megretski (Eds.), Princeton University Press, ISBN 978-0-691-11748-5, pages 326-329, 2004

2002c
Title: High-order variations for families of vector fields
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: SIAM Journal on Control and Optimization, 43(1), pages 301-324, 2004
Journal version: Download

2002b
Title: Geometric local controllability: second-order conditions
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: Proceedings of 41st IEEE Conference on Decision and Control, December 2002, pages 368-369
Conference proceedings version: Download

2002a
Title: Vector-valued quadratic forms in control theory
Author(s): Francesco Bullo, Jorge Cortes, Andrew D. Lewis, and Sonia Martinez
Detail: Sixty Open Problems in Mathematical Systems and Control Theory, Vincent Blondel and Alexandre Megretski (Eds.), Princeton University Press, ISBN 978-0-691-11748-5, pages 315-320, 2004

2001d
Title: Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
Author(s): Francesco Bullo, Andrew D. Lewis, and Kevin M. Lynch
Detail: Proceedings of MTNS02, University of Notre Dame, August 2002

2001c
Title: Kinematic controllability and motion planning for the snakeboard
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: IEEE Transactions on Robotics and Automation 19(3), pages 494-498, 2003 (IEEE copyright)
Journal version: Download

2001b
Title: A high order sufficient condition for local controllability
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: Proceedings of 40th IEEE Conference on Decision and Control, December 2001, pages 2607-2612
Conference proceedings version: Download

2001a
Title: Geometric first-order controllability conditions for affine connection control systems
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: Proceedings of 40th IEEE Conference on Decision and Control, December 2001, pages 4216-4221
Conference proceedings version: Download

2000c
Title: Time-optimal control of two simple mechanical systems with three degrees of freedom and two inputs
Author(s): A. Theo Coombs
Detail: MSc Thesis, Queen's University

2000b
Title: On the homogeneity of the affine connection model for mechanical control systems
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: Proceedings of the 39th IEEE Conference on Decision and Control, December 2000, pages 1260-1265 (IEEE copyright)
Journal version: Download

2000a
Title: The category of affine connection control systems
Author(s): Andrew D. Lewis
Detail: Proceedings of the 39th IEEE Conference on Decision and Control, December 2000, pages 5119-5124
Conference proceedings version: Download

1999a
Title: Affine connection control systems
Author(s): Andrew D. Lewis
Detail: IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control

1998c
Title: Configuration controllability of simple mechanical control systems
Author(s): Andrew D. Lewis and Richard M. Murray
Detail: SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 41(3), pages 555-574, 1999 (Note: This paper is a watered down, easier to read, version of a paper with the same title which appeared in the SIAM Journal on Control and Optimization.)
Journal version: Download

1998b
Title: When is a mechanical control system kinematic?
Author(s): Andrew D. Lewis
Detail: Proceedings of the 38th IEEE Conference on Decision and Control, December 1999, pages 1162-1167
Journal version: Download

1998a
Title: Towards F=ma in a general setting for Lagrangian mechanics
Author(s): Andrew D. Lewis
Detail: Annales Henri Poincaré 1(3), pages 569-605, 2000
Journal version: Download

1997b
Title: Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
Author(s): Francesco Bullo, Naomi E. Leonard, and Andrew D. Lewis
Detail: IEEE Transactions on Automatic Control 45(8), pages 1437-1454, 2000 (IEEE copyright)
Journal version: Download

1997a
Title: Simple mechanical control systems with constraints
Author(s): Andrew D. Lewis
Detail: IEEE Transactions on Automatic Control 45(8), pages 1420-1436, 2000 (IEEE copyright)
Journal version: Download

1996d
Title: Affine connections and distributions
Author(s): Andrew D. Lewis
Detail: Appears as ``Affine connections and distributions with applications to nonholonomic mechanics'' in Reports on Mathematical Physics 42(1/2), pages 135-164, 1998 (Proceedings for the workshop on Non-Holonomic Constraints in Dynamics held in Calgary in August 1997)
Journal version: Download

1996c
Title: Local configuration controllability for a class of mechanical systems with a single input
Author(s): Andrew D. Lewis
Detail: Proceedings of the 1997 European Control Conference

1996b
Title: Configuration controllability of mechanical systems on Lie groups
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: Proceedings of MTNS '96

1996a
Title: Decompositions of control systems on manifolds with an affine connection
Author(s): Andrew D. Lewis and Richard M. Murray
Detail: Systems & Control Letters 31(4), pages 199-205, 1997
Journal version: Download

1995e
Title: Aspects of Geometric Mechanics and Control of Mechanical Systems
Author(s): Andrew D. Lewis
Detail: Ph.D. Thesis, defended 21 April, 1995, CDS Technical Memorandum CIT-CDS 95-017

1995d
Title: The geometry of the Gibbs-Appell equations and Gauss's Principle of Least Constraint
Author(s): Andrew D. Lewis
Detail: Reports on Mathematical Physics 38(1), pages 11-28, 1996
Journal version: Download

1995c
Title: Configuration controllability of simple mechanical control systems
Author(s): Andrew D. Lewis and Richard M. Murray
Detail: SIAM Journal on Control and Optimization 35(3), pages 766-790, May 1997
Journal version: Download

1995b
Title: The mechanics of undulatory locomotion: the mixed kinematic and dynamic case
Author(s): James P. Ostrowski, Joel W. Burdick, Andrew D. Lewis, and Richard M. Murray
Detail: Proceedings of the 1995 IEEE International Conference on Robotics and Automation, May 1995, pages 1945-1951 (IEEE copyright)
Conference proceedings version: Download

1995a
Title: Configuration controllability for a class of mechanical systems
Author(s): Andrew D. Lewis and Richard M. Murray
Detail: Proceedings of the 34th IEEE Conference on Decision and Control, December 1995, pages 1-5
Conference proceedings version: Download

1994a
Title: Variational principles for constrained systems: theory and experiment
Author(s): Andrew D. Lewis and Richard M. Murray
Detail: The International Journal of Nonlinear Mechanics 30(6), pages 793-815, 1995
Journal version: Download

1993a
Title: Nonholonomic mechanics and locomotion: the snakeboard example
Author(s): Andrew D. Lewis, James P. Ostrowski, Joel W. Burdick, and Richard M. Murray
Detail: Proceedings of the 1994 IEEE International Conference on Robotics and Automation, May 1994, pages 2391-2400 (IEEE copyright)
Conference proceedings version: Download

1991d
Title: Determining optimal points of membership with dependent variables
Author(s): Kevin N. Otto, Andrew D. Lewis, and Erik K. Antonsson
Detail: Fuzzy Sets and Systems 60(1), pages 19-24, 1993
Journal version: Download

1991c
Title: Approximating α-cuts with the vertex method
Author(s): Kevin N. Otto, Andrew D. Lewis, and Erik K. Antonsson
Detail: Fuzzy Sets and Systems 55(1), pages 43-50, 1993
Journal version: Download

1991b
Title: Membership induced on manifolds by vector fields and flows
Author(s): Kevin N. Otto, Andrew D. Lewis, and Erik K. Antonsson
Detail: Fuzzy Sets and Systems 70(1), pages 15-29, 1995
Journal version: Download

1991a
Title: Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
Author(s): Andrew D. Lewis
Detail: Letters in Mathematical Physics 25(3), pages 189-201, 1992
Journal version: Download

1990a
Title: Further numerical studies of oblique impact
Author(s): Robert J. Rogers and Andrew D. Lewis
Detail: Journal of Sound and Vibration 141(3), pages 507-510, 1990
Journal version: Download

1988a
Title: Experimental and numerical study of forces during oblique impact
Author(s): Andrew D. Lewis and Robert J. Rogers
Detail: Journal of Sound and Vibration 125(3), pages 403-412, 1988
Journal version: Download

Andrew D. Lewis (andrew at mast.queensu.ca)