dψMestel(r[, R0, V0, epsilon])

the Mestel potential derivative.

Miyamoto_DF(E, L)

Miyamoto distribution function for Kuzmin-Toomre disc.

IsoDiscKal_DF(E, L)

Kalnajs distribution function for isochrone disc.

IsoDiscPLB_ndDFdJ(n1, n2, E, L, ndotOmega)

Kalnajs DF derivative w.r.t. the actions J.

Zang_outer_tapering_dL(L[, Rout, V0, mu])

Zang outer tapering derivative.

Ω1circular(dψ,d2ψ,a)

radial frequency for circular orbits, from the epicyclic approximation a is the semi-major axis (equivalent to r for a circular orbit)

EFromAE(ψ,dψ,a,e,params)

energy as a function of (a,e) for a given potential ψ (and its derivatives)

ELFromAE(ψ,dψ,a,e,params)

combined energy + angular momentum as a function of (a,e) for a given potenial ψ (and its derivatives)

ComputeActionsAE(ψ,dψ,a,e,params)

FrequenciesFromαβ(α,β,Ω₀)

converts frequencies ratios to frequencies

Getϖ(ω,n1,n2,dψ,d2ψ,params)

translate a complex frequency into a rescaled frequency. maps $\omega \to [-1,1]$

Fouvry & Prunet B3

@ASSUMPTION: - ω is dimensionless, that is, rescaled by Ω₀ already.

Getϖ(ω,ωmin,ωmax)

ϖ version with ωmin, ωmax

FindVbound(n1,n2,dψ,d2ψ,Ω₀,rmin,rmax)

find any valid non- 0 or 1 v value at u=-1 or u=1

RcircFromΩ2circ(Ω₂,dψ,d2ψ,rmin,rmax[,tolx,tolf])

perform backwards mapping from Omega_2 for a circular orbit to radius

@ASSUMPTIONS: - Ω2circular is a decreasing function of radius - d2ψ used for value at 0.

compute the dimensionless function for Omega2 from (a,e) (Fouvry 21 eq. G7)

the wrapped Theta derivative function

translate From (sp,sa) to (E,L)

NonAsciiHandle(x)

convert some extra unicode characters to ascii

GetResLinesJL(ω,ψ,dψ,d2ψ,Kv,tabresonances)