Quick Answer
Calculate Lyapunov Stability Margin for Nonlinear Small-Angle Pendulum Perturbations
Calculator
Result Interpretation
Lyapunov Stability Margin for Nonlinear Small-Angle Pendulum Perturbations calculator computes Lyapunov Stability Margin in rad using the defined engineering formula and the input values provided.
Worked Example
Verified calculation
Given:
- Mass Moment of Inertia = 0.4
- Damping Coefficient = 0.2
- Cubic Stiffness Coefficient = 10
- Gravitational Torque Coefficient = 9.81
Expected Result:
- Lyapunov Stability Margin = 1.3971444957841
Engineering Interpretation:
Under the given input conditions, the calculated result is: Lyapunov Stability Margin = 1.3971444957841 rad.
The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from automatically validated test cases.
Formula / Method
lyapunov stability margin = sqrt(2.0 * gravitational torque coefficient / cubic stiffness coefficient) * (1.0 - (damping coefficient * damping coefficient) / (4.0 * mass moment of inertia * gravitational torque coefficient))Formula family: formula_simulation_pendulum_system_stability_margin_analyzer_for_nonlinear_small_angle_perturbations
Variables
| Symbol | Label | Role | Description |
|---|---|---|---|
| mass_moment_of_inertia_kg_m2 | Mass Moment of Inertia | INPUT | Mass Moment of Inertia |
| gravitational_torque_coefficient_N_m_rad | Gravitational Torque Coefficient | INPUT | Gravitational Torque Coefficient |
| cubic_stiffness_coefficient_N_m_rad3 | Cubic Stiffness Coefficient | INPUT | Cubic Stiffness Coefficient |
| damping_coefficient_N_m_s_per_rad | Damping Coefficient | INPUT | Damping Coefficient |
| lyapunov_stability_margin | Lyapunov Stability Margin | OUTPUT | Lyapunov Stability Margin |
Calculation Steps
- Enter the mass moment of inertia in kg·m².
- Enter the gravitational torque coefficient in N·m/rad.
- Enter the cubic stiffness coefficient in N·m/rad³.
- Enter the damping coefficient in N·m·s/rad.
- Step 1: Compute lyapunov stability margin.
- Read the lyapunov stability margin (rad) from the results.
Engineering Summary
Calculate Lyapunov Stability Margin for Nonlinear Small-Angle Pendulum Perturbations
Frequently Asked Questions
What does this calculator calculate?
The Lyapunov Stability Margin for Nonlinear Small-Angle Pendulum Perturbations calculator estimates Lyapunov Stability Margin based on the input parameters you provide
Why is mass moment of inertia important in this calculation?
mass moment of inertia is directly proportional to lyapunov stability margin. When you enter mass moment of inertia in kg·m², the calculator uses it in the engineering formula to compute the output
How should I interpret the result lyapunov stability margin?
The calculator outputs lyapunov stability margin in rad. The result is computed directly from the input values using the defined engineering formula
What units should I use for the inputs?
Enter each value in the units shown next to the input field: Mass Moment of Inertia (kg·m²), Gravitational Torque Coefficient (N·m/rad), Cubic Stiffness Coefficient (N·m/rad³), Damping Coefficient (N·m·s/rad). Make sure all inputs use the specified units for consistent results
What assumptions does this calculator use?
This calculator uses automatically validated engineering formulas. Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment
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