Nonlinear dynamics — Pendulum 90 Period

Nonlinear dynamicsPASS · <0.01%

Transient nonlinear dynamics, impact, and conservation-law verification. Checks: amplitude-dependent pendulum period.

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Problem statement

Geometry: Point mass on a massless rigid link L=1 m, g=9.81 m/s2, released from rest at theta0=pi/2.
Material: Constitutive or analytical definition: T=4 sqrt(L/g) K(sin(theta0/2)).
Boundary conditions: Required solver capability: transient_large_rotation. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Exact nonlinear period=2.36784194758 s; small-angle period 2.00606668071 s must not be used as the target.

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

units m
pendulum length=1.0 theta0=1.57079632679 gravity=9.81
solve transient method=symplectic dt=0.0001 t_end=3.0
extract period

Reference value	T_exact=2.367842 s
Our result	T_sim=2.368000 s
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	Rigid pendulum L=1 m released from 90 deg, elliptic integral K(1/sqrt(2))

Updated: 2026-10-27 · version not recorded