1. The problem statement, all variables and given/known data Hi guys! I am reading a paper on inverted pendulum. However, I cant understand the dynamics equations of this inverted pendulum. You may look at the images below. Basically the thruster is placed at top plate, while the middle plate is a base plate where pivot is placed. And then bottom plate is where you place your counterweight. Upon thruster firing, the pendulum arm will rotate. The equations are attached in the pictures below. I(T) and I(CW) represent the moments of inertia of the thruster and counterweight respectively. My question is, can any one help me explain these equations? I understand that the left side is the net force on horizontal direction based on newton's second law, and the left side has the thrust caused by pivots stiffness, weight and thrust. However, I dont understand where the momentum of inertia * angular acceleration / arm length comes in. 2. Relevant equations Relevant equations for this question will be newton's second law, and also rotational dynamics. 3. The attempt at a solution My attempt at understanding the equations are stated in the question part.