TY - JOUR
T1 - Resonances in a continuously forced anharmonic oscillator
AU - Zharnitsky, Vadim
N1 - Funding Information:
I would like to thank Mark Levi for suggestingt his problem to me and for many helpful discussions. This work was supportedb y Air Force Office of Scientific Researchu nderG rant No. F49620-92-J-0049DEF and by the Departmento f Energy.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1997/1/13
Y1 - 1997/1/13
N2 - 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.
AB - 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.
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U2 - 10.1016/S0375-9601(96)00833-X
DO - 10.1016/S0375-9601(96)00833-X
M3 - Article
AN - SCOPUS:0042078511
VL - 224
SP - 264
EP - 270
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 4-5
ER -