- A comprehensive formulation of mechanics from ``first principles''
using differential geometric methods.

**Reference:***The physical foundations of geometric mechanics*. - 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
relative equilibria.

**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
mechanics.

**Reference:***Towards*.*F=ma*in general setting for Lagrangian mechanics - 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
are characterised.

**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 snakeboard example*. - 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*.