Back to my research page.
- A comprehensive formulation of mechanics from ``first principles''
using differential geometric methods.
Reference: The physical foundations of geometric
- An apology for geometric mechanics written for a robotics audience.
Reference: Is it worth learning differential geometric methods
for modelling and control of mechanical systems?
- A Riemannian geometric formulation of reduction and stability of
Reference: Reduction, linearization, and stability of relative
equilibria for mechanical systems on Riemannian manifolds.
- A genuinely Galilean setting for rigid body mechanics which seems
strangely absent from the literature.
Reference: Rigid body mechanics in Galilean spacetimes.
- A general setting for Lagrangian mechanics using the ``Lagrange
two-force.'' This is a quite general presentation of Lagrangian
Reference: Towards F=ma in general setting for
- An investigation of Lagrangian foliations of the zero energy levels of
central force problems.
Reference: Lagrangian submanifolds and an application to the
reduced Schrödinger equation in central force problems,
- Affine connections preserving the kinetic energy of a Riemannian metric
Reference: Energy-preserving affine connections.
- A thorough investigation of how affine connections can be used to
describe the unforced equations of motion for a system with constraints
linear in velocity. Note that the use of an affine connection to describe
constrained mechanical systems dates back as far as the work of Synge
(Geodesics in nonholonomic geometry Math. Ann. 99 738-751,
1928). Other authors have since picked up this thread, and my efforts have
been motivated by work of Peter Crouch and Tony Bloch.
Reference: Affine connections and distributions.
- A variational principle for nonlinear constraints, and a Noether theorem
for these systems.
Reference: Variational principles for nonlinearly constrained
systems in one independent variable.
- A generalisation of the Gibbs-Appell method from systems of particles
and rigid bodies to general Lagrangians, along with the relationship of these
to Gauss's Principle of Least Constraint.
Reference: The geometry of the Gibbs-Appell equations and
Gauss's Principle of Least Constraint.
- An investigation of the ``snakeboard'' example.
Reference: Nonholonomic mechanics and locomotion: the
- A theoretical and experimental investigation of variational methods,
wherein the value of the vakonomic equations are put in doubt, as concerns
their description of solutions for mechanical systems.
Reference: Variational principles for constrained systems:
theory and experiment.
Andrew D. Lewis (andrew at mast.queensu.ca)