Dynamics of a Rotated Orthogonal Gravitational Wedge Billiard

The paper states that trajectories are dense when TA/TB is irrational and that periodic orbits occur for θ* = arctan(p/q), but the density claim is only asserted via a one-dimensional approximation and a heuristic time-map argument (equations (13)–(16)) without a rigorous torus-flow proof; it also contains minor inconsistencies (e.g., ũ(t) uses cos(ϕ) instead of cos(θ) in (8b)) and an imprecise use of tAj+1 = 2 j TA that obscures whether these are absolute times or increments . By contrast, the model cleanly constructs exact normal-distance coordinates dA, dB with constant accelerations −sin θ and −cos θ (no approximation), shows the two “clocks” evolve as a linear flow on T2, proves minimality for irrational slopes and density in the accessible set QE, and recovers the periodic case (including the p and q collision counts and the initial momentum (ū*, w̄*)) in a self-contained way, matching the formulas reported in the paper (11), (12), and (17) .