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>
40 lines
1.7 KiB
Python
40 lines
1.7 KiB
Python
import numpy as np
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from rosette import *
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np.set_printoptions(precision=4)
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print("== equal ring, no centre: max Re(eig) (log vs newton)")
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for n in range(2,10):
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out=[]
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for law in ('log','newton'):
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X,C,Rc=config(n,1,1,1,0) # A ring only: build n bodies
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X=X[:n];C=C[:n];Rc=Rc[:n]
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w2,_=omega2(law,X,C,Rc,0)
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m,_=stability(law,X,C,Rc,w2); out.append(m)
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print(n, "log w2r2=%.4f"%omega2('log',X,C,Rc,0)[0], "maxRe log %.2e newton %.2e"%tuple(out))
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print("== log twisted alternating 2n-gon: closed form vs direct sum, stability")
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for n in (2,3,4,5,6):
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for mu in (1,0.9,0.7,0.5,0.3,0.1,0.01):
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r,w2=closed_log_twisted(n,mu)
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rs=roots('log',n,1,mu,np.pi/n)
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X,C,Rc=config(n,1,mu,r,np.pi/n)
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d,wa,wb,t=resid('log',n,1,mu,r,np.pi/n)
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m,_=stability('log',X,C,Rc,wa)
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print(f"n={n} mu={mu:<5} rho={r:.5f} w2*ra^2={w2:.5f} direct_roots={[round(x,5) for x in rs]} resid={d:.1e} tang={t:.1e} maxRe={m:.2e} massratio(m^0.2)={mu**5:.3g}")
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print("== newton twisted alternating")
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for n in (3,4,6):
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for mu in (1,0.7,0.5,0.3,0.1,0.01):
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rs=roots('newton',n,1,mu,np.pi/n)
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res=[]
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for r in rs:
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X,C,Rc=config(n,1,mu,r,np.pi/n); d,wa,wb,t=resid('newton',n,1,mu,r,np.pi/n)
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m,_=stability('newton',X,C,Rc,wa); res.append((round(r,5),round(wa,4),f"{m:.1e}"))
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print(f"n={n} mu={mu} roots(rho,w2,maxRe)={res}")
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print("== aligned (twist 0) nested")
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for law in ('log','newton'):
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for n in (3,6):
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for mu in (1,0.5,0.1):
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rs=roots(law,n,1,mu,0.0)
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res=[]
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for r in rs:
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X,C,Rc=config(n,1,mu,r,0.0); d,wa,wb,t=resid(law,n,1,mu,r,0.0)
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m,_=stability(law,X,C,Rc,wa); res.append((round(r,5),f"{m:.1e}"))
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print(law,n,mu,res)
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