SimplePendulum

SimplePendulum(
    var_name='simple_pendulum',
    L=1.0,
    g=9.81,
    damping=0.0,
    state_variables=None,
    diagnostic_variables=None,
    *args,
    **kwargs,
)

Nonlinear pendulum with optional linear damping.

Parameters

var_name : = 'simple_pendulum'

Human-readable label.

L : = 1.0

Pendulum length in metres. Must be > 0.

g : = 9.81

Gravitational acceleration in m/s². Must be > 0.

damping : = 0.0

Linear damping coefficient λ (s⁻¹). damping=0 gives undamped SHM.

state_variables : = None

Names for [angle, angular velocity].

diagnostic_variables : = None

Names for post-integration diagnostics.

Notes

State variables are theta (angle, rad) and omega (angular velocity, rad/s) in that order. Diagnostic variables energy and omega_0 are computed after integration.

Examples

import matplotlib.pyplot as plt
from climatecritters.model_critters.pendulum import SimplePendulum

model = SimplePendulum(L=1.0, g=9.81, damping=0.1)
output = model.integrate(t_span=(0, 20), y0=[1.5, 0.0], method='RK45')
ts = output.to_pyleo(var_names=['theta'])
ts.plot()
plt.savefig('docs/reference/figures/SimplePendulum_example.png',
            dpi=150, bbox_inches='tight')

SimplePendulum example output

Methods

Name	Description
damping_ratio	Return ζ = λ / (2ω₀). ζ < 1 underdamped, ζ = 1 critical.
natural_frequency	Return ω₀ = √(g/L) in rad/s.
natural_period	Return T₀ = 2π/ω₀ in seconds (small-angle approximation).

damping_ratio

SimplePendulum.damping_ratio()

Return ζ = λ / (2ω₀). ζ < 1 underdamped, ζ = 1 critical.

natural_frequency

SimplePendulum.natural_frequency()

Return ω₀ = √(g/L) in rad/s.

natural_period

SimplePendulum.natural_period()

Return T₀ = 2π/ω₀ in seconds (small-angle approximation).