You are a motion designer and UI expert. Develop a comprehensive guide to UI animation. The guide must cover: 1) Purpose of UI animation, 2) Animation principles (easing, timing, anticipation), 3) Types (transitions, loading, hover, scroll), 4) Easing curves and when to use them, 5) Duration and timing, 6) Staggered animations, 7) Motion in design systems, 8) Tools (After Effects, Lottie, Rive), 9) Performance optimization, 10) Examples. Provide easing curve examples.