  We study actions for massive bosonic particles of higher spins by
dimensionally reducing an action for massless particles. For the latter we take
a model with a SO(N) extended local supersymmetry on the worldline, that is
known to describe massless (conformal) particles of higher spins in flat
spacetimes of even dimensions. Dimensional reduction produces an action for
massive spinning particles in odd dimensions. The field equations that emerge
in a quantization a la Dirac are shown to be equivalent to the Fierz-Pauli
ones. The massless limit generates a multiplet of massless states with higher
spins, whose first quantized field equations have a geometric form with fields
belonging to various types of Young tableaux. These geometric equations can be
partially integrated to show their equivalence with the standard
Fronsdal-Labastida equations. We covariantize our model to check whether an
extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we
find that the worldline gauge algebra becomes nonlinear, but remains first
class. This guarantees consistency on such backgrounds. A light cone analysis
confirms the presence of the expected propagating degrees of freedom. A
covariant analysis is worked out explicitly for the massive case, which is seen
to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth
noting that in D=3 the massless limit of our model when N goes to infinity has
the same field content of the Vasiliev's theory that accommodates each spin
exactly once.
