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>
17 lines
679 B
Python
17 lines
679 B
Python
import numpy as np
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from rosette import *
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def hess(law,X,C):
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N=len(X); D=np.zeros((2*N,2*N))
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for i in range(N):
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for j in range(N):
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if i==j: continue
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d=X[j]-X[i]; s=np.hypot(*d); I=np.eye(2); dd=np.outer(d,d)
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B = C[j]*(I/s**2-2*dd/s**4) if law=='log' else C[j]*(I/s**3-3*dd/s**5)
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D[2*i:2*i+2,2*j:2*j+2]+=B; D[2*i:2*i+2,2*i:2*i+2]-=B
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return D
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def maxre(law,X,C,w2):
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N=len(X); w=np.sqrt(w2); D=hess(law,X,C)+w2*np.eye(2*N)
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J=np.zeros((2*N,2*N))
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for i in range(N): J[2*i,2*i+1]=1; J[2*i+1,2*i]=-1
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A=np.block([[np.zeros((2*N,2*N)),np.eye(2*N)],[D,2*w*J]])
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return np.max(np.linalg.eigvals(A).real)
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