# 陀螺进动 - Gyroscopic Precession

带角动量、力矩和章动的交互式3D可视化

> 标准页面: https://elysiatools.com/zh/visualizations/gyroscopic-precession

- **分类:** Physics

## 概述

Interactive 3D gyroscope precession simulation demonstrating conservation of angular momentum, torque, and nutation. Features angular momentum L = Iω, torque τ = dL/dt = r × mg, precession rate Ω = mgr/(Iω), and moment of inertia I = ½mr². Real-time 3D visualization with pseudo-isometric projection showing spinning disk with radial spokes, tilt axis with pivot point, precession motion around vertical axis, optional nutation oscillation, and golden tip trail. Vector display with green angular momentum L (along spin axis), red torque τ (perpendicular to L and mg), and blue gravity mg vectors. Energy tracking with rotational KE = ½Iω², gravitational PE = mgh, and total energy conservation demonstration. Charts include energy (KE/PE/total), angular velocities (spin vs precession rate), and nutation angle over time. Adjustable parameters: spin velocity ω (10-100 rad/s), initial tilt angle θ (10-60°), mass m (0.1-2.0 kg), disk radius r (0.05-0.3 m), axle length L (0.1-0.5 m), gravity g (1.6-20 m/s²), inertia factor (0.5-2x), simulation speed (0.1-3x), toggle for vectors/nutation/trail. Applications in navigation systems, bicycle stability, Earth's axial precession (26,000 year cycle), and fundamental physics from atoms to galaxies. Multi-language support (zh, en, es, fr, de, ru, pt).

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