ANALYSIS OF DRY FRICTION DYNAMICS IN A VIBRO-IMPACT ENERGY HARVESTER

The paper derives a three-equation reduced system for 1:1 orbits without sliding (its eq. (4.6)), obtained by integrating the two branches between impacts (Γ±), enforcing the impact law, and imposing periodicity; the candidate solution reproduces exactly this construction, including the same F1/F2 primitives and the same algebraic relations and periodicity T=2 for f(t)=cos(πt+φ) . For the bifurcation thresholds, the paper defines dΣ, dss, dc, and dΓ` via interior zeros of Ẑ and Filippov tangency/crossing conditions on Σ and zero pre-impact speed on Γ` (eqs. (4.7), (4.20), (4.21), (4.22)), which match the candidate’s implicit conditions and classifications; the paper further adds natural monotonicity/orientation inequalities that the candidate notes qualitatively . Overall, both arguments coincide in method and conclusions.