Periodically forced motion of a classical particle in a one-dimensional potential with superquadratic growth at infinity is considered. It is shown that an arbitrary amount of energy can be transmitted to the oscillator by exciting the system with a continuous time-periodic forcing. This result extends Littlewood's example of unbounded motions in the presence of a discontinuous periodic forcing and, thus, sheds light on the relation between the smoothness of forcing and the stability of motion. A new version of the averaging procedure, which had to be applied to justify the construction, is outlined.
|Original language||English (US)|
|Number of pages||7|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - Jan 13 1997|
ASJC Scopus subject areas
- Physics and Astronomy(all)