... integrals of the motion, which contain derivatives of the variables of one order lower than the order of the differential equations The most celebrated of these first integrals is that of conservation of ... are the vibration modes φi (x) of the system, K and M as defined by (1.75) and (1.77) are both diagonal, because of the orthogonality of the mode shapes, and a set of decoupled equations is obtained ... recognize the form of the mass and stiffness matrices, except that the shape functions ψi (x) 34 Lagrangian dynamics of mechanical systems are defined over the entire structure and satisfy the geometric...