# 复摆 - Double Pendulum

探索经典力学中的混沌运动

> 标准页面: https://elysiatools.com/zh/visualizations/double-pendulum

- **分类:** Physics

## 概述

Explore chaotic motion in classical mechanics through an interactive double pendulum simulation. Features RK4 numerical integration for accurate energy conservation, real-time visualization of pendulum motion with velocity-colored trails (blue→red gradient), phase space plots (θ vs ω) showing chaotic attractors, and butterfly effect demonstration with 3 pendulums differing by 0.001 rad. Adjustable parameters: lengths l₁, l₂ (0.5-2.0 m), masses m₁, m₂ (0.5-5.0 kg), gravity g (1-20 m/s²), damping coefficient (0-0.5), and initial angles θ₁, θ₂ (-π to π). Preset configurations: horizontal (max potential energy), vertical (stable equilibrium), inverted (unstable equilibrium), and random. Real-time statistics display: time t, angles θ₁, θ₂, angular velocities ω₁, ω₂, kinetic energy T, potential energy V, and total energy E. Theory section includes Lagrangian mechanics derivation, equations of motion, chaos theory explanation, historical context (Lagrange 1788, Poincaré 1890s, Nature 2002), and observation guide. Demonstrates sensitive dependence on initial conditions, nonlinear coupling, and energy conservation. Perfect for physics education, chaos theory introduction, and classroom demonstrations. Multi-language support (zh, en, es, fr, de, ru, pt).

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