pendulum_nonlinear_ode

pendulum_nonlinear_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

pendulum_nonlinear_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

pendulum_nonlinear_ode_test

matlab_ode, MATLAB codes which set up various ordinary differential equations (ODE).

Reference:

• Augusto Belendez, Carolina Pascual, David Mendez, Tarsicio Belendez Vazquez, Cristian Neipp,
  Exact solution of the nonlinear pendulum problem,
  Revista Brasileira de Ensino de Fisica,
  Volume 29, Number 4, pages 645-648, 2007.
• Karlheinz Ochs,
  A comprehensive analytical solution of the nonlinear pendulum,
  European Journal of Physics,
  Volume 32, pages 479-490, 2011.

Source Code:

• pendulum_nonlinear_conserved.m, evaluates a quantity that should be conserved by the nonlinear pendulum ODE.
• pendulum_nonlinear_deriv.m, evaluates the right hand side of the ODE.
• pendulum_nonlinear_exact.m, returns the exact solution of the nonlinear pendulum ODE; however, it only returns the first component, and the result is only valid if the initial angular velocity is zero.
• pendulum_nonlinear_parameters.m, returns parameters of the ODE.
• pendulum_nonlinear_period.m, returns the period of the ODE.