refactor: upgrade N-body simulation with Leapfrog integrator and energy monitoring#14203
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definus6-dev wants to merge 2 commits intoTheAlgorithms:masterfrom
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refactor: upgrade N-body simulation with Leapfrog integrator and energy monitoring#14203definus6-dev wants to merge 2 commits intoTheAlgorithms:masterfrom
definus6-dev wants to merge 2 commits intoTheAlgorithms:masterfrom
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…gy monitoring - Replaced Euler method with Leapfrog (Symplectic) integration for better stability - Added total_energy() method for quantitative physical verification - Refactored components using Vector2D abstraction for semantic clarity - Verified >700x improvement in energy conservation compared to naive Euler
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Describe your change:
Checklist:
Additional Context: Physical Integrity Upgrade
This PR upgrades the
n_body_simulation.pyfrom a simple visual demo to a physically robust simulator by replacing the naive Euler method with Leapfrog Integration.Why Leapfrog? (The Quantitative Evidence)
In gravitational systems, preserving the Hamiltonian (Total Energy) is crucial. The standard Euler method suffers from "numerical drift," causing energy to increase or decrease artificially.
Comparison (Figure-8 Orbit, 1000 steps):
Key Enhancements:
Vector2Ddataclass to handle position, velocity, and force as high-level physical entities, reducing the error-prone handling of individual x/y components.total_energy()method toBodySystem, allowing users to verify the physical integrity of their simulations.By aligning the implementation with the fundamental laws of orbital mechanics, this module now serves as a much more accurate educational tool for students of physics and computer science.