Then, generate function handles that are the input to ode45. Because ode45 accepts only first-order systems, reduce the system to a first-order system. Numerically solve these equations by using the ode45 solver. The nonlinear equations of motion are second-order differential equations.
Step 7: Solve Nonlinear Equations of Motion The kinetic energy of the pendulum is enough to overcome gravitational energy and enable the pendulum to make a full loop. The pendulum always moves in one angular direction. The higher energies of the contour plot do not close upon themselves. The kinetic energy of the pendulum is not enough to overcome gravitational energy and enable the pendulum to make a full loop. The pendulum swings back and forth between two maximum angles and velocities. The lower energies of the contour plot close upon themselves. The figure shows two regions of distinct behavior. The constant energy contours are symmetric about the θ axis and d θ / d t axis, and are periodic along the θ axis.
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