Nonlinear mechanical resonators combined with piezoelectric transducers are widely used in vibration energy harvesting applications for their broadband behavior. Such nonlinear vibration energy harvesters may exhibit various orbits for a given excitation, each of them being associated with a given harvested power. Thus, in order to optimize the harvested power, it is crucial to find ways to jump from low power orbits to high power orbits, and to remain on them as long as possible. In this paper, we present a mathematical framework to test and study how effective is a given orbit jump strategy. Starting from the analytical model of a Duffing-type nonlinear mechanical energy harvester, we describe some of its dynamics, and we introduce a command function that can be used to impact the dynamics of the harvester. Thereafter, we will test and evaluate a set of command functions based on sinusoidal current injection.