Bulirsch-Stoer-Instability

Bulirsch-Stoer instability in ORSA visualised with Java Plotly.

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Figure 1. Eccentricity variation for Jupiter (low amplitude) and Saturn (high amplitude) over 200,000 years, from Runge-Kutta integration. Analytical approximations are overlaid as dotted lines. The results of Runge-Kutta integration in legacy ORSA correspond to the analytical approximations, albeit with a growing divergence over time. Adapted from Stenborg (2024), below.

Figure 2. Eccentricity variation for Jupiter (low amplitude) and Saturn (high amplitude) over 200,000 years, from Bulirsch-Stoer integration. Analytical approximations are overlaid as dotted lines. The results of Bulirsch-Stoer integration in legacy ORSA diverge significantly from the analytical approximations (e.g., amplitude, period, vertical shift). Adapted from Stenborg (2024), below.

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Key Files

• EccentricitySimulation.java    A Java program for visualising orbital element variation with the Tablesaw wrapper for Plotly.
  
• ORSA_Output.csv    Jovian and Saturnian eccentricity and inclination evolution data, as calculated via analytical means, and as simulated using Runge-Kutta and Bulirsch-Stoer integration in ORSA.
  
• pom.xml     Maven dependencies to make Tablesaw available, specified as a Project Object Model.

Software Requirements

• Java.
  
• Java IDE, e.g., Eclipse (optional).
  

Reference

Stenborg, TN 2024, "Bulirsch-Stoer Instability in ORSA with Java Plotly Visualisation", in BV Hugo, R Van Rooyen and OM Smirnov (eds), ADASS XXXI, ASP, Orem, UT, pp. 461–464.