Datum: time-domain dynamics, jerk, hodograph & export#670
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Session 6 — release the driver and run the mechanism under its own physics.
- solver/dynamics.ts: single-DOF Eksergian equation of motion
I(θ)θ̈ + ½I′θ̇² = τ − cθ̇ − V′, with I(θ), I′(θ), V′(θ) built from the exact
first/second-order kinematic coefficients and lumped rod masses; substepped
RK4 integrator. A live "Release & run" mode + Dynamics panel (gravity/density/
damping/torque sliders, kinetic+potential+total energy read-out and plot).
- solver/ad3.ts: cubic-dual {v,d1,d2,d3} AD backend (a 4th instantiation of the
one residual algebra, atan2 exact to 3rd order) → the jerk field x‴(θ), with
the mixed term recovered by polarising three hyper-dual passes.
- Hodograph (velocity-vector-tip locus) + velocity-ratio / dead-point readout.
- model/export.ts: solved sketch → vector SVG and real DXF (LINE/CIRCLE/ARC +
sampled-spline LWPOLYLINE), motion profile → CSV.
- Self-tests 32 → 41: dynamics vs closed-form pendulum θ̈=−(g/L)cosθ (2e-8),
energy conservation (3e-9·mgL), monotone damped dissipation, I′ vs finite-diff,
static equilibrium, jerk vs finite-diff of acceleration (2.7e-5), SVG/DXF/CSV
fidelity. Verified headless in Chromium (0 console errors) + verify-project.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BzHyorzzwSMikwadDgjdyQ
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Session 6 — Datum comes alive
Datum already tells you where a driven mechanism sits and how fast it moves (exact velocity + acceleration off the constraint Jacobian). This session lets go of the crank: give the links mass and the mechanism runs under its own physics — a four-bar falls, swings, overshoots and settles under gravity, no driver.
The physics (the elegant part)
A well-constrained driven mechanism has exactly one degree of freedom, so its whole configuration is an implicit function
x(θ)of a single generalized coordinate. The exact first- and second-order kinematic coefficients from Session 5 (x'=J⁺e_driver,x'') are precisely what a one-DOF Lagrangian needs, so the entire dynamics collapse to a single scalar ODE — the classical Eksergian equation of motion:Each RHS eval is one re-solve + one kinematics pass — machinery Datum already owns. Mass is lumped honestly (each link a uniform rod, mass split to its endpoints), making it a bona-fide Lagrangian system whose total energy is conserved exactly.
What's new
solver/dynamics.ts— the Eksergian EOM assembler + a substepped RK4 integrator; a live "Release & run" mode and a Dynamics panel (gravity / density / damping / torque sliders, kinetic+potential+total energy read-out and an energy-vs-time plot where T and V trade off while E stays flat — the visual proof of conservation).solver/ad3.ts— a cubic-dual{v,d1,d2,d3}AD backend (a fourth instantiation of the one residual algebra,atan2carried exactly to third order) giving the jerk fieldx‴(θ) = J⁺(−3x'ᵀHx″ − x'ᵀTx'x'), the mixed term recovered by polarising three hyper-dual passes; plotted alongside speed/accel for cam smoothness.model/export.ts— the solved sketch to vector SVG (exact Béziers & arcs) and a real DXF (LINE / CIRCLE / ARC entities + sampled-spline LWPOLYLINEs, opens in any CAD), and the motion profile to CSV.Verification
Self-test suite 32 → 41, each re-deriving a claim from an independent reference:
θ̈=−(g/L)cosθ— worst 2e-8I′(θ)vs finite-diff ofI(θ)(~5e-5)arcGeomVerified end-to-end headless in Chromium (four-bar swings under gravity, energy plot live, all three exports download valid files, hodograph + jerk curve render, 0 console errors) plus
node scripts/verify-project.mjs datum-cad-9r4k(scope + conformance + lint + build all green).🤖 Generated with Claude Code
https://claude.ai/code/session_01BzHyorzzwSMikwadDgjdyQ
Generated by Claude Code