The nonlinear pendulum always oscillates

Abstract

It is shown that the nonlinear pendulum equation can be transformed into a linear harmonic oscillator in the phase space thanks to Kerner’s method [12]. Moreover, as a mathematical divertissement, the second-order differential equation determining the phase-space trajectories of the nonlinear pendulum is quantized.

Keywords:

• Lie and Noether symmetries
• Jacobi last multiplier
• Lagrangians
• quantization

2000 Mathematics Subject Classification:

• 76M60
• 37Jxx
• 70S10
• 81S05