This paper discusses the properties of simple strategies for swinging up an inverted pendulum using energy control. It shows that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategies provides insights into the robustness of minimum time solutions. The paper presents a simple strategy for swinging up the pendulum by controlling its energy. The key result is that the global behavior of the swing-up is completely characterized by the ratio n of the maximum acceleration of the pivot to the acceleration of gravity. For example, one swing is sufficient if n is larger than 4/3. The analysis also gives insight into the robustness of minimum time swing-up in terms of energy overshoot. The paper discusses energy control strategies for swinging up a pendulum, showing that controlling the energy of the pendulum can be more effective than directly controlling its position and velocity. The energy of the uncontrolled pendulum is given by E = ½J(θ̇)² + mgl(cosθ - 1). To perform energy control, it is necessary to understand how the energy is influenced by the acceleration of the pivot. The paper presents a control strategy based on the Lyapunov method, which drives the energy towards its desired value. The control law is given by u = k(E - E₀)θ̇cosθ, which ensures that the energy is controlled effectively. The paper also discusses different swing-up behaviors, including single-swing double-switch, single-swing triple-switch, and multi-swing behaviors. The number of swings required depends on the maximum acceleration of the pivot. For example, if the maximum acceleration is smaller than 4g/3, the pendulum must swing several times before reaching the upright position. The paper also discusses the generalization of energy control to more complex systems, such as multiple pendulums on a cart. The paper concludes that energy control is a convenient way to swing up a pendulum, and the behavior of such systems depends critically on the maximum acceleration of the pivot.This paper discusses the properties of simple strategies for swinging up an inverted pendulum using energy control. It shows that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategies provides insights into the robustness of minimum time solutions. The paper presents a simple strategy for swinging up the pendulum by controlling its energy. The key result is that the global behavior of the swing-up is completely characterized by the ratio n of the maximum acceleration of the pivot to the acceleration of gravity. For example, one swing is sufficient if n is larger than 4/3. The analysis also gives insight into the robustness of minimum time swing-up in terms of energy overshoot. The paper discusses energy control strategies for swinging up a pendulum, showing that controlling the energy of the pendulum can be more effective than directly controlling its position and velocity. The energy of the uncontrolled pendulum is given by E = ½J(θ̇)² + mgl(cosθ - 1). To perform energy control, it is necessary to understand how the energy is influenced by the acceleration of the pivot. The paper presents a control strategy based on the Lyapunov method, which drives the energy towards its desired value. The control law is given by u = k(E - E₀)θ̇cosθ, which ensures that the energy is controlled effectively. The paper also discusses different swing-up behaviors, including single-swing double-switch, single-swing triple-switch, and multi-swing behaviors. The number of swings required depends on the maximum acceleration of the pivot. For example, if the maximum acceleration is smaller than 4g/3, the pendulum must swing several times before reaching the upright position. The paper also discusses the generalization of energy control to more complex systems, such as multiple pendulums on a cart. The paper concludes that energy control is a convenient way to swing up a pendulum, and the behavior of such systems depends critically on the maximum acceleration of the pivot.