Geometric mechanics

1. A geometric approach to the comparison of the variational approach to constrained mechanics with the Lagrange-D'Alembert Principle
   Reference: Nonholonomic and constrained variational mechanics
2. A comprehensive formulation of mechanics from ``first principles'' using differential geometric methods
   Reference: The physical foundations of geometric mechanics
3. 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?
4. 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
5. A genuinely Galilean setting for rigid body mechanics which seems strangely absent from the literature
   Reference: Rigid body mechanics in Galilean spacetimes
6. 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
7. 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
8. Affine connections preserving the kinetic energy of a Riemannian metric are characterised
   Reference: Energy-preserving affine connections
9. 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
10. A variational principle for nonlinear constraints, and a Noether theorem for these systems
    Reference: Variational principles for nonlinearly constrained systems in one independent variable
11. 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
12. An investigation of the ``snakeboard'' example
    Reference: Nonholonomic mechanics and locomotion: the snakeboard example
13. 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