Kinematic Analysis of Elytra Flight as a Discrete Dynamical System: Energy Injection and Perpetual Motion in Minecraft Physics
{"We":[0],"analyse":[1],"the":[2,26,36,61,64,77,83,86,93,96,117,139,167,201,207,212],"Elytra":[3],"gliding":[4,94],"mechanic":[5],"in":[6,91],"Minecraft":[7],"as":[8,200],"a":[9,15,31,137,172],"discrete":[10],"dynamical":[11],"system":[12],"defined":[13],"by":[14,211],"20":[16],"Hz":[17],"Euler-forward":[18],"velocity":[19],"integrator.":[20],"For":[21],"every":[22,105,144],"constant":[23,145],"pitch":[24,106,152,177],"θ,":[25],"per-tick":[27],"map":[28,87],"F_θ":[29],"admits":[30],"unique":[32],"attracting":[33],"fixed":[34,62,102,140],"point;":[35],"asymptotic":[37],"glide":[38],"ratio":[39],"is":[40,88,116],"maximised":[41],"at":[42,143],"θ":[43,113],"=":[44,48,70,114,124,130,134],"0,":[45],"where":[46],"R(0)":[47,123],"10.102:1":[49],"with":[50,57,76,120,166],"terminal":[51],"horizontal":[52],"speed":[53],"30.20":[54],"m/s,":[55],"consistent":[56,75],"community":[58],"documentation.":[59],"At":[60],"point":[63,141],"Jacobian":[65],"has":[66],"spectral":[67],"radius":[68],"ρ":[69],"0.99,":[71],"predicting":[72],"linear":[73],"convergence":[74],"numerically":[78],"observed":[79],"1863":[80],"ticks.":[81],"Under":[82],"planar":[84],"reduction":[85],"piecewise":[89],"affine":[90],"both":[92],"and":[95,107,126,132],"climbing":[97],"regime.":[98],"This":[99],"yields":[100],"closed-form":[101],"points":[103],"for":[104,159,163],"hence":[108],"an":[109],"analytic":[110],"proof":[111],"that":[112],"0":[115,131],"global":[118],"optimum,":[119],"exact":[121],"value":[122],"495/49":[125],"one-sided":[127],"slopes":[128],"R′(0⁺)":[129],"R′(0⁻)":[133],"284229/12250.":[135],"As":[136],"corollary,":[138],"descends":[142],"pitch,":[146],"so":[147],"altitude":[148,189],"gain":[149,190],"requires":[150],"dynamic":[151],"cycling.":[153],"The":[154],"asymmetric":[155],"momentum-transfer":[156],"coefficients":[157],"(0.1":[158],"dive":[160],"versus":[161],"0.128":[162],"climb),":[164],"combined":[165],"Euler":[168],"integration":[169],"scheme,":[170],"create":[171],"net":[173,188],"energy-injection":[174],"mechanism.":[175],"Dynamic":[176],"cycling":[178],"(\\"dolphining\\")":[179],"exploits":[180],"this":[181],"asymmetry":[182],"to":[183],"achieve":[184],"+3.66":[185],"blocks":[186],"of":[187],"per":[191],"cycle.":[192],"A":[193],"coefficient":[194,204],"sweep":[195],"identifies":[196],"c_L*":[197],"≈":[198],"0.1261":[199],"critical":[202],"lift":[203],"below":[205],"which":[206],"dolphining":[208],"schedule":[209],"found":[210],"greedy":[213],"search":[214],"becomes":[215],"dissipative.":[216],"Simulation":[217],"code:":[218],"https://gitlab.com/geoywang/elytra-flight":[219]}
Authors
- Yujia Wang (ORCID: https://orcid.org/0009-0006-8068-0801)
Institutions
- New York University (US)
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