Contact selection chaos of two analytical Gömböcs under biharmonic vertical excitation
- 1Faculty of Civil Engineering, RWTH Aachen University, Mies-van-der-Rohe-Straße 1, 52074, Aachen, Germany
Abstract
Chaotic rocking of homogeneous Gömböc bodies on a vertically excited support is investigated by explicitly embedding two analytical Gömböc morphologies within a spherical radial surface description. The instantaneous contact point is obtained from a global height minimization over the rotated surface, which couples attitude evolution to a contact selection mechanism that can switch between competing minimizing branches. Under biharmonic vertical excitation, this coupling generates strong nonlinearity and leads to period multiplication, intermittency, crisis transitions, and strange attractors. The two analytical morphologies, distinguished by their phase functions on the spherical parameter domain, produce different contact-branch organizations and therefore different routes to chaotic responses under identical forcing conditions. Chaotic behavior is characterized using stroboscopic Poincaré sampling and maximal Lyapunov exponents, and its onset is related to separatrix splitting in a reduced near-saddle description. The results indicate that smooth mono-monostatic morphology can act as an intrinsic chaos generator through contact selection rather than through impacts or multi-contact constraints.
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BibTeX
@article{feng2026contact,
title = {{Contact selection chaos of two analytical Gömböcs under biharmonic vertical excitation}},
author = {Dong Feng},
journal = {Chaos Solitons \& Fractals},
year = {2026},
month = may,
doi = {10.1016/j.chaos.2026.118539},
url = {https://doi.org/10.1016/j.chaos.2026.118539},
note = {CC BY},
}
RIS
TY - JOUR
TI - Contact selection chaos of two analytical Gömböcs under biharmonic vertical excitation
AU - Dong Feng
PY - 2026
DA - 2026/05/19
JO - Chaos Solitons & Fractals
DO - 10.1016/j.chaos.2026.118539
UR - https://doi.org/10.1016/j.chaos.2026.118539
AB - Chaotic rocking of homogeneous Gömböc bodies on a vertically excited support is investigated by explicitly embedding two analytical Gömböc morphologies within a spherical radial surface description. The instantaneous contact point is obtained from a global height minimization over the rotated surface, which couples attitude evolution to a contact selection mechanism that can switch between competing minimizing branches. Under biharmonic vertical excitation, this coupling generates strong nonlinearity and leads to period multiplication, intermittency, crisis transitions, and strange attractors. The two analytical morphologies, distinguished by their phase functions on the spherical parameter domain, produce different contact-branch organizations and therefore different routes to chaotic responses under identical forcing conditions. Chaotic behavior is characterized using stroboscopic Poincaré sampling and maximal Lyapunov exponents, and its onset is related to separatrix splitting in a reduced near-saddle description. The results indicate that smooth mono-monostatic morphology can act as an intrinsic chaos generator through contact selection rather than through impacts or multi-contact constraints.
SN - 0960-0779
SN - 1873-2887
ER -