In this paper we consider the following class of Lagrangian systems:
Lε,μ(q, ̇q,Q, ̇Q,t)= ̇Q22+ ̇q22+ε(1−cosq)+μf(q, ̇q,Q, ̇Q,t,μ)
which has been studied by many authors in connection with Arnold's diffusion. Extending [2] prove, by variational means, that, for suitable perturbations including for example:
f(q, ̇q,Q, ̇Q,t,μ)=(1−cosq)(cosQ+cost)+μp−1sin(q+Q)(p>2)
if μ is small enough, exists a diffusion orbit of Lε,μ such that ̇Q(t) undergoes a variation of order 1 in a time td polinomial in μ, td≈1μ2.
