The talk will be roughly in three parts, with the last two strongly related.
In the first part of the talk I shall discuss the use of affine connections
for writing the equations of motion for ``simple'' mechanical systems with
constraints (i.e., those whose Lagrangians are kinetic energy minus potential
energy). The second part of the talk deals with using the Gibbs-Appell
equations to arrive at equations of motion for general Lagrangian systems
(here general means formulated on a bundle over the **R** and with
nonlinear constraints). In the last part of the talk, I remain in the
general framework and talk about variational principles, first Gauss's
Principle of Least Constraint, then a generalisation of the
Lagrange-d'Alembert Principle.

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