7.12* Lagrange's equations in the form discussed in this chapter hold only if the forces (at least the nonconstraint forces) are derivable from a potential energy. To get an idea how they can be modified to include forces like friction, consider the following: A single particle in one dimension is subject to various conservative forces (net conservative force = F = -OU/ax) and a nonconservative force (let's Problems for Chapter 7 283 R Figure 7.12 Problem 7.14 call it Ffric). Define the Lagrangian as L = 7 - U and show that the appropriate modification is ac d ac + Ffric = ax dt ax