Resonant Angle Libration Span
Unwrap successive resonant angles using the shortest step and measure their sampled half-range; cadence must resolve steps below 180 degrees and a short span does not prove libration.
Description
An angular time series crossing 360 degrees can be unwrapped by taking the shortest successive angular step.
An angular time series crossing 360 degrees can be unwrapped by taking the shortest successive angular step. Its sampled half-range describes the observations, but a short record does not prove resonant libration rather than slow circulation.1
Unwrap successive resonant angles using the shortest step and measure their sampled half-range; cadence must resolve steps below 180 degrees and a short span does not prove libration.
When to use Resonant Angle Libration Span
Use this tool to unwrap successive resonant angles using the shortest step and measure their sampled half-range; cadence must resolve steps below 180 degrees and a short span does not prove libration.
Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Resonant Angle Libration Span and understand its results
- Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter angleDegrees using the field table and calculation rules, then run the tool.
- Read unwrappedDegrees, sampledHalfAmplitudeDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| angleDegrees | Angle degrees | list of number | Required |
Enter a nonempty finite angleDegrees list in observation order. The first angle is wrapped into [0,360); each next difference is mapped to the shortest signed step and accumulated. An exactly half-turn step is rejected as directionally ambiguous. The tool returns the unwrapped list and sampled half-range; a single sample has half-amplitude zero.
unwrapped_i = unwrapped_(i−1) + shortest signed step; halfAmplitude = (max−min)/2 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| unwrappedDegrees | Unwrapped degrees | list of number |
| sampledHalfAmplitudeDegrees | Sampled half amplitude degrees | number |
{
"input": {
"angleDegrees": [
350,
355,
0,
5,
10
]
},
"output": {
"unwrappedDegrees": [
350,
355,
360,
365,
370
],
"sampledHalfAmplitudeDegrees": 10
}
}Limitations and assumptions
Sampling must resolve actual successive motion below 180 degrees to avoid aliasing. No timestamps, resonance definition, period fit or libration flag are evaluated. Measurement uncertainty and near-half-turn floating-point behavior require caller judgment; the result concerns only the supplied window.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Tisserand Orbital Parameter: Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded. For a complementary task, use Soi Handoff Hysteresis: Apply caller-defined sphere-of-influence handoff hysteresis to a sampled trajectory; boundaries are not universal force-dominance limits.
References
-
Resonant Angle Libration Span — tool.io
Similar or alternative tools
- Tisserand Orbital Parameter
Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.
- Soi Handoff Hysteresis
Apply caller-defined sphere-of-influence handoff hysteresis to a sampled trajectory; boundaries are not universal force-dominance limits.