  A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew,
for constructions of dynamics on general algebroids. One obtains formalisms
similar to the Lagrangian and the Hamiltonian ones. In contrast with recently
studied concepts of Analytical Mechanics on Lie algebroids, this approach
requires much less than the presence of a Lie algebroid structure on a vector
bundle, but it still reproduces the main features of the Analytical Mechanics,
like the Euler-Lagrange-type equations, the correspondence between the
Lagrangian and Hamiltonian functions (Legendre transform) in the hyperregular
cases, and a version of the Noether Theorem. Besides, the constructions seem to
be more natural and simpler.
