  Van Holten's covariant algorithm for deriving conserved quantities is
presented, with particular attention paid to Runge-Lenz-type vectors. The
classical dynamics of isospin-carrying particles is reviewed. Physical
applications including non-Abelian monopole-type systems in diatoms, introduced
by Moody, Shapere and Wilczek, are considered. Applied to curved space, the
formalism of van Holten allows us to describe the dynamical symmetries of
generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry
and applied to the SUSY of the monopoles. Yet another application concerns the
three-dimensional non-commutative oscillator.
