Nonlinear dynamics — Pendulum Energy

Nonlinear dynamicsPASS · <0.01%

Transient nonlinear dynamics, impact, and conservation-law verification. Checks: long-time energy conservation and phase error.

Tolerance:: 5%

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Problem statement

Geometry: Same 90-degree pendulum, no damping, integrate for 100 exact periods.
Material: Constitutive or analytical definition: E=0.5 L^2 theta_dot^2+gL(1-cos theta)=constant.
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: Initial and exact total energy per unit mass=9.81 J/kg; linear and angular momentum constraints remain consistent with the hinge reaction.

WebCAE Terminal

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 damping=0
solve transient method=symplectic dt=0.002 periods=100
extract energy_conservation

Results comparison

Reference value	E=9.810000 J/kg over 100 periods
Our result	E=9.810078 J/kg (drift=0.0008%)
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	90-deg pendulum integrated for 100 complete periods (~236.8 s)

Updated: 2026-10-27 · version not recorded