Power and energy as systemic properties — Part II: Mechanical systems

We consider mechanical systems with external terminals and on each terminal a force acting and the position. This paper is a companion paper to work of Willems (2013) which deals with electrical circuits. The central question asked is what the power and the energy is delivered from the environment to the mechanical system. We show that power and energy are well defined concepts only when the set of interacting terminals form a port, that is, when the sum of the forces acting on the terminals is zero. We show that the classical mechanical building blocks, as a spring, a damper, a connector, and an inerter are ports, but that a mass is not a port. This is in contrast with electrical circuits, where all the classical building blocks are ports. We also examine the energy stored in mechanical systems, and derive a formula for the motion energy stored in a set of moving masses. We finally contrast Lagrangian dynamics with modeling using the `tearing, zooming, and linking´ methodology.