Welcome to Pendulum Bond Graph Model

As discussed in the page on pendulum mechanics the main functional objects of the pendulum are Support, Rod, Particle and Gravity . We will model them by Bond Graph word models. We use the component titles the names of the objects, and add the corresponding power and control ports (see Figure below).

We insert a power port at the top of Support component. It represents the action of Support restricting Rod component rotation. In addition, there is an output control port, which delivers the angular velocity of the pendulum.

Rod has two power ports, the top and bottom ones, and two input control ports. The lower power port is connected by a bond to the upper Support's power port, and thus transmit its effect on Rod. The upper power ports represent the actions of the Rod on the Particle. The side control inputs deliver information necessary for transformation described in the page on pendulum mechanics.

Particle also has two power ports, one on the top and the other on the bottom of the component. The bottom port is connected by a bond to the upper Rod's power port and thus represents interactions between these components. The upper port is on the other hand connected by another bond to Gravity component. The last component represents the particl's weight, which acts to Particle. There are also two control output ports, which deliver the positions of the particle P.

Note we have assumed the initial positive power transfer from Support and Gravity to Particle. Of course during the motion this changes. Thus, at the beginning, the particle is at the highest position, and its velocity is zero. Hence we assume that the potential energy is initially at the maximum, and the kinetic energy is zero. When released the potential energy starts reducing as the particle height goes down. On the other hand the velocity of the particle, and its kinetic energy increases until it reaches the lowest position. When the potential energy is at minimum the particle velocity and hence its kinetic energy is at the maximum. Hence, during this motion the power delivered to the particle is positive. After passing through the vertical pendulum starts swinging on the other side. The particle starts rising and hence the transfer of the power to the particle is negative until it reaches zero velocity again. If there is no friction this happens at the same height from which the particle was released, and the process repeats itself.

We start developent of pendulum Bond Graph model from Support component. By clicking the right link button we open the corresponding component's document.