OrbitClassifier Class

class galport.OrbitClassifier(t, angles, theta_p=None, time_resolution=5.0)

Bases: object

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A class for classifying orbits based on their resonant angle behavior.

This classifier analyzes the time evolution of a resonant angle to determine whether an orbit is in resonance, passing through resonance, or non-resonant. It supports multiple resonance families commonly found in barred galaxies.

Parameters:

• t ((N,) numpy.ndarray) – Array of time values.

• angles ((M, N, 3) or (M, N,) or (N,) numpy.ndarray) – Series of angles. Can be one of: - Full set of 3 angles (θ_R, θ_z, θ_φ) for M orbits - Pre-computed resonant angle(s) for one or multiple orbits

• theta_p ((N,) numpy.ndarray, optional) – Array of the perturbation (e.g., bar) rotation angle. Required for families that use θ_p. Default: None (assumes θ_p = 0)

• time_resolution (float, optional) – Time resolution for angle analysis. The time series is downsampled to approximately this resolution to reduce numerical noise. Recommended not to set too small. Default: 5.0

Classification Types

The classifier assigns one of the following types to each orbit:

Type	Name	Description
0	Not classified	Unable to determine type
1	Increasing angle	Monotonically increasing (ω_res > 0)
2	Decreasing angle	Monotonically decreasing (ω_res < 0)
3	Resonance around 0	Librating around θ_res = 0
4	Resonance around π	Librating around θ_res = π
5	Passage through 0 (ω>0 → ω<0)	Crossing resonance at θ=0, slowing down
6	Passage through π (ω>0 → ω<0)	Crossing resonance at θ=π, slowing down
7	Passage through 0 (ω<0 → ω>0)	Crossing resonance at θ=0, speeding up
8	Passage through π (ω<0 → ω>0)	Crossing resonance at θ=π, speeding up

Resonance Families

Different resonance families correspond to different combinations of angles. The following families are supported:

Family	Resonance Angle Formula
'ILR'	\(\theta_{\text{res}} = 2(\theta_\varphi - \theta_p) - \theta_R\)
'corotation'	\(\theta_{\text{res}} = (\theta_\varphi - \theta_p) + \pi/2\)
'uha'	\(\theta_{\text{res}} = 4(\theta_\varphi - \theta_p) - \theta_R\)
'vILR'	\(\theta_{\text{res}} = \theta_z - \theta_R\)

Orbit Types by Family:

• ILR: Type 3 → x1 orbits, Type 4 → x2 orbits

• Corotation: Type 3 → L4 points, Type 4 → L5 points

• vILR: Type 4 → banana orbits

t

Downsampled time array.

Type:

numpy.ndarray

angles

Downsampled angle array(s).

Type:

numpy.ndarray

theta_p

Downsampled perturbation angle array.

Type:

numpy.ndarray

n_ang

Number of angle series (1 or M).

Type:

int

__call__(t_out, family='ILR', time_around_res=False, amplitude_res=False)

Find resonant type

Parameters:

• t_out (float or (N, ) numpy array) – array of times, in which we define the orbital type

• family (str ('ILR')) –

  List of families:

  • ’ILR’ or ‘ilr’ : θres = 2(θφ - θp) - θR

  ILR orbits if resonance around 0 - x1 orbits, around π - x2; * ‘corotation’ or ‘cor’ : θres = θφ - θp + π/2 Corotatation orbits if resonance around around 0 - L4, π - L5 orbits; * ‘ultraharmonic’ or ‘uha’ or ‘4:1’ : θres = 4(θφ - θp) - θR * ‘vILR’ or ‘vilr’ : θres = θz - θR ILR orbits if resonance around pi - banana orbits;

• time_around_res (bool, optional) – if True function estimate the resonance entry and exit times for resonant orbits, by default False

• amplitude_res (bool, optional) – if True function estimate the maximum libration amplitude of the resonant angle, by default False

Returns:

• types ((M, ) numpy array) – array of types (integer)

• amplitude ((M, ) numpy array, optional) – array of angles amplitude for passage or resonant orbit.

• times ((M, 2) numpy array, optional) – if time_around=True array of times for resonance and passage orbits, when they entered/left into resonance or began/end to pass through it.

__init__(t, angles, theta_p=None, time_resolution=5.0)

Initialise angles

Parameters:

• t ((N, ) numpy array) – array of times

• angles ((M, N, 3) or (M, N, ) or (N, ) numpy array) – series of 3 angles (θR, θz, θφ) or resonant angle, which user defined

• theta_p ((N, ) numpy array, optional) – array of the perturbation (e.g. bar) rotation angle Default: None

• time_resolution (float, optional) – time accuracy of series. Recommend don’t take too small Default: 5.