Launch-video motion

Inside a shot, things arrive on an exponential settle whose time constant is chosen per move — about 0.1-0.15 s for an object, ~0.43 s for Raycast's four-frame-height crane and 0.6-0.8 s for the two measured counters — and leave on the mirror curve. Nothing decorative moves on a UI object. Overshoot, velocity blur and camera drift are register choices with measured base rates, and a film reads as lively because of creep, accelerating rhythm and causes that ignite their effects, not because anything bounces. This is the 2.4.0 four-rule motion system, split out of launch-video-seams and corrected against 29 Skale films, 18 acclaimed films and HeyGen's source.

Settle exponentially; size tau to the travel

Write the curves once and pass tau as a parameter:

const TAU = 0.131;
const eo = (dur, tau = TAU) => (p) => (1 - Math.exp(-p * dur / tau)) / (1 - Math.exp(-dur / tau));
const ei = (dur, tau = TAU) => (p) => 1 - eo(dur, tau)(1 - p);

• Objects, ~0.1-0.15 s. HeyGen's 02-bouncy-ui declares tau 0.131 s in its header but never calls that constant: its moves pass their own, 0.04-0.18 s (median ~0.11 s; 0.135 for the flip, 0.168 for a growth). 01-ui-sting's 1 - 2^(-10p) works out to ~0.146 s at its median 1.01 s tween. Skale's Replit Parallel Agents decays its opening slam word's drift ×0.78 per frame at 29.97 fps (tau 0.134 s), and Poke '7' whip-scrolls at tau 0.13-0.15 s both ways. 03-message-sting runs faster: it writes each move as 1 - 2^(-10t/T) with settle times T of 0.12-0.53 s, a tau of 0.02-0.08 s.
• Longer travel settles slower. Raycast's crane covers ~4 frame heights with a half-life of ~0.3 s (tau ~0.43 s, n = 1), while Apple Liquid Glass's snap pull-back settles at tau ~0.2 s; the counters in Taste Labs and Contra Indy settle at tau 0.6-0.8 s (n = 2).
• Shipped durations over 2,064 HeyGen tweens: median 0.35 s (p25 0.20, p75 0.55); by ease, power2.out 0.26 s, power3.out 0.46, expo.out 0.50.
• Exits by seam type, not a fixed ratio: HeyGen's run 36-82 % of the entry (zoom exits 0.18-0.22 s against 0.5 s entries; cut-the-curve pairs 69-82 %). A mirrored letter-by-letter un-type can run as long as the entry or longer (Extend: 0.43 s in, 0.5 s out, ~116 %; n = 1). Inside a HyperFrames project, motion-doctrine's exit at ~75 % of the entry and the seam stamp's timings win.

GSAP's expo.out differs from 1 - 2^(-10p) by at most 0.78 % of travel: it matters for exact mirrors and pixel replicas, not for feel.

Cameras are the exception

A camera may run at constant velocity and be cut mid-drift. Linear Agent drifts 1.2-4 % of the frame per second on each axis, with identical displacement every 0.25 s and no ease at either end; Apple Liquid Glass's shots open mid-drift and accelerate to 1.26× by 400 ms. HeyGen's none ease (313 of 2,284 non-set tweens, median 0.85 s) is drifts and progress fills. Drive a camera from one progress channel and derive the rest: claude-design-send sets scale = 1 + 0.48a and x = -(scale - 1) × 118, pinned on the column the eye tracks, because a push and a pan on two eases read as two movements. A drift continues the entry vector. Never start a new pan or push in a scene's back half; product-launch-video's rule 3 bans even a slow one there, so inside a project keep creep to the entry's continuation. Never put a spring or back ease on a camera: the whole frame sways.

Overshoot is a register

Visible overshoot appears in 4 of 29 Skale films (Replit Slides' liquid glyph, Replit Parallel Agents' tile tilt, Bevel's check mark, Contra x fal's trophy pill) and 3 of 18 acclaimed (Apple Liquid Glass's toggle swelling mid-travel, Claude Cowork's mark at ~2×, Notion 3.0's face). HyperFrames defaults an entrance to power3.out or a critically damped springEase, allows 0.80-0.85 damping for an iOS feel (~1-1.5 % overshoot) and 0.60-0.70 only when playful; motion-doctrine forbids bounce and elastic but allows back.out(1.4-1.7) on an entry; HeyGen's claude-paper frame law says settle, never bounce. The bouncy-sting register is 02-bouncy-ui: zeta 1/3 on three channels of one body, position 1.45 Hz, shape 1.88 Hz, rotation 2.5 Hz, the lighter channel ringing faster. HyperFrames calls damping under 0.55 cartoon wobble, so inside a project use zeta 1/3 only when the brief names the sting (hyperframes-reconciliation). As a GSAP ease windowed to end at rest:

const spring = (dur, f = 1.45, z = 1 / 3) => (p) => {
  const u = p * dur, wd = 2 * Math.PI * f * Math.sqrt(1 - z * z);
  return 1 - Math.exp(-2 * Math.PI * z * f * u) * Math.cos(wd * u) * (1 - p);
};

01-ui-sting's lockup rides one decaying sine, A · e^(-t/0.279) · sin(2πt/0.5) (2 Hz, zeta ~0.27), with the symbol on +A and the word on −A, so the two parts spring away from each other on landing and come to rest together; its endcard reuses the spring at a smaller amplitude.

Blur

• Derived for element moves. It rides the move's own ease and peaks at peak speed. Size the peak to the subject: 10 px on text, 18-20 px on a full-frame surface. HeyGen's 481 blur targets cluster at 8 px (×64) and 20 px (×45); 207 resolve to 0. Blur the wrapper, never its children, and never blur and fade in one tween. CSS blur scales with transform: a raw 2 px reads as ~16 px at ×8.
• Sharp is also a choice. Velocity blur shows in only 9 of 29 Skale films and 6 of 18 acclaimed. Poke '7' whips ~20 % of frame height per frame completely crisp; Notion Mail snaps to ×2.4 in 5 frames with no blur.
• Authored focus is a scene tool. Arrive defocused and sharpen in 4-8 frames (9 Skale films: the Poke anthology, Taste Labs, Replit Canvas, Adaline, Bevel, Poke '7', Contra Indy, Contra x fal, Conduit), or resolve rows from blur ~0.25 s apart (Linear Agent). The rack-focus cut lives in launch-video-cuts.

Stamp decisions, ease curves

Glyph flipbooks, typed runs, odometer digits, clicks and highlight hops are per-frame sets; slides, scales and settles are tweens. Never tween a decision; it reads as a smear. tl.set is 1,162 of HeyGen's 3,446 calls, a third, and 10 of 18 acclaimed films stamp single-frame decisions: Granola 2.0 swaps pages in one 60 fps frame every ~1.0-1.15 s; Raycast hops its selection one click at a time over one S-curve pan. The sound sits on the stamps (sound-from-motion).

Holds

No float, pulse or breathe on a UI object: none of the 18 acclaimed films and no Skale film does it, and motion-doctrine treats a scene that finishes entering early as missing story, not missing wobble. A hold may carry a slow camera push or drift (10 of 29 Skale films, among them T:0, Bud, all three Replit films and Conduit; drift or creep in 10 of 18 acclaimed); HeyGen keeps it on the entry vector. It may also carry status motion only while the system works (Claude Cowork drifts 18-50 px/s on the agent's turn, under 10 px in 2.5 s on the user's), ambient brand light, or a living background plate that never stops (one linear master tween) and makes its big shift ~0.1 s before each scene change (HeyGen's inspector-launch). HyperFrames' product-launch-video would rather hold still with a small jitter; inside a project keep jitter off UI objects and creep only as the entry's continuation (hyperframes-reconciliation). Test: pause anywhere; something meaningful is mid-flight, or the frame is a deliberate hold.

Rhythm and causes

A montage runs legible, then accelerating, then a blur zone, and snaps to a hold: timeline-launch's prompt firehose steps 3 prompts at 0.42 s, 6 at 0.17 s and ~20 at 0.07 s while blur ramps 0 → 2 px, then snaps off on the hold. Before a climax, hold 0.3-0.75 s of stillness, the picture half of the pre-reveal subtraction in launch-video-sound. A cause visibly launches its effect: click, squash, release, flight, impact. Inside a HyperFrames project each effect starts on its causing frame (motion-doctrine's causal motion); outside one, a click may let its press read first (launch-video-ui-demo). Anticipation, freeze, release is the strongest form; HeyGen's liquid pop builds pressure on power3.in (scaleX 1 → 1.1, scaleY 1 → 0.78), freezes everything for 0.4 s, then ruptures on power4.in in 0.2 s. Cursor mechanics also live in that UI-demo node; cut cadence belongs to launch-video-cuts, stagger cadence to launch-video-type.

When to apply

Every shot of a launch film, sting or README film. UI-scale springs stay in spring-animations and UI easing in easing-curves; inside a HyperFrames project the seam stamp's eases and exit timings win, and hyperframes-reconciliation settles overshoot, blur and hold motion.

Gotcha

A spring on every arrival reads as a toy, and a breathe loop on a held card reads as the video waiting. The films called lively are lively because the camera creeps, the rhythm accelerates and every cause visibly launches its effect; bounce is not what makes them lively.

Sources

• HeyGen, hyperframes-launches (Apache-2.0): heygen-apple-motion/02-bouncy-ui/index.html L92-128, L474-480 (per-move taus L450-822); 01-ui-sting/index.html L283-291, L356-361, L496-505; 03-message-sting/index.html L332-434; claude-paper-launch/FRAME-claude.md L469-470, L619; claude-design-send-hyperframes-launch/HANDOFF.md §12.1; timeline-launch/compositions/act2b-spiral.html L306-380; inspector-launch/DESIGN.md "Motion Rules" and index.html L2433-2437, L2634-2644; liquid-brand-refraction/js/liquid-pop-v2.js L445-525. Tween census by HKTITAN (147 de-duplicated composition files, 3,446 calls; blur targets and per-ease medians over all 161 composition files): heygen_corpus_stats.py and tables/heygen.md in docs/research/launch-films/.
• heygen-com/hyperframes (Apache-2.0): .agents/skills/motion-doctrine/SKILL.md (causal motion, no idle wobble, stillness before climax, timing intents) and .agents/skills/cut-the-curve/SKILL.md (Blur logic), repo-internal and not installed by npx skills add; skills/product-launch-video/references/motion-language.md (rule 3); skills/hyperframes-animation/adapters/gsap-easing-and-stagger.md (Spring Eases), rules/spring-pop-entrance.md, rules/3d-camera-flight.md.
• Skale (skale.solutions/portfolio) films by client, and the acclaimed films (Linear Agent, Raycast, Apple Liquid Glass, Claude Cowork, Notion Mail, Notion 3.0, Granola 2.0), measured by HKTITAN 2026-09-28: docs/research/launch-films/ (notes/synthesis-skale.md, notes/synthesis-acclaimed.md, metrics/).