c981537904
Eyes facts for aetheria-gravity: regular and twisted alternating polygon equilibria (log closed form, Newtonian sources), linear stability (Muscas-Pasca-Stoica log thresholds reproduced, Klemperer, Thomson), the soft core's reach, PeriodAround's ring rule against the twisted equilibrium spin, and rotating-frame stationary points against the drawn potential. Solver scripts beside the note. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
21 lines
1.1 KiB
Python
21 lines
1.1 KiB
Python
import numpy as np
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from rosette import *
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from stab import *
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print("== soft core at game numbers: hexagon (n=3 twisted), c_heavy=304.9, R_heavy=79.8 (median sun); mu=c_l/c_h, R_l=R_h*mu^1.25")
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ch,Rh=304.9,79.8
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for mu in (1.0,0.7,0.555):
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Rl=Rh*mu**1.25
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rlog,_=closed_log_twisted(3,mu)
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for ra in (30,60,100,200,1000,3000):
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rs=roots('soft',3,ch,ch*mu,np.pi/3,lo=0.2,hi=5,N=3000,ra=ra,Ra=Rh,Rb=Rl)
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out=[]
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for r in rs:
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d,wa,wb,t=resid('soft',3,ch,ch*mu,r,np.pi/3,ra=ra,Ra=Rh,Rb=Rl)
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rb=r*ra; sep=np.sqrt(ra**2+rb**2-ra*rb)
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out.append(f"rho={r:.4f} T={2*np.pi/np.sqrt(wa):.1f}s v_h={np.sqrt(wa)*ra:.2f} minsep={min(sep,ra*np.sqrt(3)):.0f}")
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print(f"mu={mu} ra={ra}: log rho={rlog:.4f} | soft: "+" ; ".join(out))
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print("== same-radius alternating (generator today): omega^2 r^2 per species, log: heavy feels (n-1)mu... ")
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for n in (2,3):
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for mu in (1,0.7,0.555):
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wh=((n-1)*1+n*mu)/2; wl=((n-1)*mu+n*1)/2
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print(f"2n={2*n} mu={mu}: w2r2 heavy={wh:.3f} light={wl:.3f} period ratio T_h/T_l={np.sqrt(wl/wh):.4f}")
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