Physical Principles & Mathematical Derivation
Unlike textbook approximations that replace sin θ with θ, our RK4 solver integrates exact sin θ dynamics — letting you verify mass independence while observing true elliptic-integral period elongation above 30°!
Questions & Concepts
What physical equation governs Simple & Large-Angle Nonlinear Pendulum Simulator?
θ̈ + (g / L) sin θ = 0, T₀ = 2π√(L / g) — Unlike textbook approximations that replace sin θ with θ, our RK4 solver integrates exact sin θ dynamics — letting you verify mass independence while observing true elliptic-integral period elongation above 30°!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.