Kinematic Analysis of Elytra Flight as a Discrete Dynamical System: Energy Injection and Perpetual Motion in Minecraft Physics

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22773063
Primary Topic
Biomimetic flight and propulsion mechanisms
Type
preprint
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preprint

Kinematic Analysis of Elytra Flight as a Discrete Dynamical System: Energy Injection and Perpetual Motion in Minecraft Physics

Yujia Wang
Zenodo (CERN European Organization for Nuclear Research)
Biomimetic flight and propulsion mechanisms
preprint

Kinematic Analysis of Elytra Flight as a Discrete Dynamical System: Energy Injection and Perpetual Motion in Minecraft Physics

Yujia Wang
preprint en

Abstract

We analyse the Elytra gliding mechanic in Minecraft as a discrete dynamical system defined by a 20 Hz Euler-forward velocity integrator. For every constant pitch θ, the per-tick map F_θ admits a unique attracting fixed point; the asymptotic glide ratio is maximised at θ = 0, where R(0) = 10.102:1 with terminal horizontal speed 30.20 m/s, consistent with community documentation. At the fixed point the Jacobian has spectral radius ρ = 0.99, predicting linear convergence consistent with the numerically observed 1863 ticks. Under the planar reduction the map is piecewise affine in both the gliding and the climbing regime. This yields closed-form fixed points for every pitch and hence an analytic proof that θ = 0 is the global optimum, with exact value R(0) = 495/49 and one-sided slopes R′(0⁺) = 0 and R′(0⁻) = 284229/12250. As a corollary, the fixed point descends at every constant pitch, so altitude gain requires dynamic pitch cycling. The asymmetric momentum-transfer coefficients (0.1 for dive versus 0.128 for climb), combined with the Euler integration scheme, create a net energy-injection mechanism. Dynamic pitch cycling ("dolphining") exploits this asymmetry to achieve +3.66 blocks of net altitude gain per cycle. A coefficient sweep identifies c_L* ≈ 0.1261 as the critical lift coefficient below which the dolphining schedule found by the greedy search becomes dissipative. Simulation code: https://gitlab.com/geoywang/elytra-flight

Zenodo (CERN European Organization for Nuclear Research)
New York University (US)
Affordable and clean energy
Biomimetic flight and propulsion mechanisms
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