Nonlinear Dynamics of Rapidly Driven Systems
Abstract
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency ω. The explicit expression for the effective Lagrangian is derived up to cal O(1/ω6) next-to-next-to-leading approximation in the strong-drive regime. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges.
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BibTeX
@misc{besharat2026nonlinear,
title = {{Nonlinear Dynamics of Rapidly Driven Systems}},
author = {Afshin Besharat and Alexander A. Penin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28996},
eprint = {2605.28996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28996},
}
RIS
TY - UNPB
TI - Nonlinear Dynamics of Rapidly Driven Systems
AU - Afshin Besharat
AU - Alexander A. Penin
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.28996
UR - https://arxiv.org/abs/2605.28996
AB - We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency ω. The explicit expression for the effective Lagrangian is derived up to cal O(1/ω^6) next-to-next-to-leading approximation in the strong-drive regime. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges.
ER -