Contact selection chaos of two analytical Gömböcs under biharmonic vertical excitation

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.