- #1

Kashmir

- 468

- 74

"First consider holonomic constraints. When we derive Lagrange's equation from either Hamilton's or D'Alembert's principle, the holonomic constraint appear in the last step when the variations in the ##q_i## were considered independent of each other. However, the virtual displacements in the ##\delta q_{I}##'s may not be consistent with constraints. If there are ##n## variables and ##m## constraint equations ##f_\alpha## of the form Eq. (1.37), the extra virtual displacements are eliminated by the method of Lagrange undetermined multipliers.

I do not understand the parts that the virtual displacements may be inconsistent with constraints because earlier on in the book he defines virtual displacement as the infinitesimal change of the coordinates *consistent with the forces and constraints imposed on the system at the given instant ##t##* (pg 16).