Symplectic Integrators & KAM Theory - Long-Time Hamiltonian Dynamics¶
- Task ID:
math.symplectic_integrators - Domain:
math - Subdomain:
numerical_odes_dynamical_systems - Status:
test - Tags:
dynamics,numerical_methods,hamiltonian_systems,chaos
Public Summary¶
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Example B1 Prompt Excerpt¶
# 2D Nonlinear Hamiltonian System and Dynamical Invariants
> **Level B1**: Full algorithm description — provides complete implementation details.
## Problem
You are investigating an unknown 2D dynamical system. Your goal is to infer the exact governing equations from noisy, sparse short-term observations, and then use those equations to perform a massive long-term integration.
We provide two data files:
1. `data/trajectory_obs.csv`: A short-term trajectory snippet containing columns `(t, x1, x2, x3, x4)`. The observations are **sparse and noisy**: at each time, some of `x1, x2, x3, x4` may be missing, and the reported values contain measurement noise.
2. `data/initial_conditions.csv`: The initial conditions for {{ n_orbits }} orbits you need to analyze (`orbit_id, x1, x2, x3, x4`).
Use the canonical interpretation `q1 = x1`, `p1 = x2`, `q2 = x3`, and `p2 = x4`.
Notes¶
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