Hi everybody! I'm struggling with a physics problem I though I had solved, but as it is turning out recently, I probably hadn't. The problem might actually be pretty easy, just me being unable to solve properly. All of you are familiar with inverted pendulum. Now, imagine an inverted pendulum with a fixed pivot point that is extensible. It can stretch itself into any length. What it does, is that it stretches itself so that the height of it's end point is always at the same height above the pivot point. In order to stretch itself, it obviously has to apply some force to the ground. You can imagine this exactly as a human when doing a step. When leaning forward, you're maintaining approximately same height above the ground. The leg touching the ground is extending according to the velocity of your body. My question is, what are the equations of motion for this thing? I want to be able to answer questions like: if I know where the body is right now, how fast it is moving and how high above the ground it is, where exactly will it be in one second? Thanks for your help!