A guide to examples and exercises from “Geometric Control of Mechanical Systems”

We list the physical systems that are considered in the book of Bullo and Lewis [2004], either as examples or as exercises. There are many other (not physical) examples in the text, and many other exercises. The intent is to provide a sampling of the sorts of systems one may treat using the methods detailed in the book, and to provide a guide as to where one can find discussions of the modeling, analysis, and control design issues for these systems. The order is that in which they appear in the book. 1. Planar rigid body: This system we saw in Section 1.1 and is depicted in Figure 1(a). This example appears in the following places, in the stated (a) The planar rigid body (b) The two-link planar manipulator Figure 1: contexts. (a) In Exercises E1.1 and E1.2 the reader is asked to derive the equa-tions of motion for this system using elementary methods, and do some simulations to test their intuition. (b) The planar body is one of a few examples that recur throughout Chapter 4 to illustrate the mathematical modeling of mechanical systems. The reader is referred to Examples 4.3, 4.7, 4.31, 4.45, and 4.53, where all aspects of the system are put into our geometric framework, from the configuration space through to the control forces for the system.