chapter  7
86 Pages

Lagrangean Mechanics Kinetics

WithJohn G. Papastavridis

This chapter continues and concludes our compact but comprehensive treatment of Lagrangean or analytical mechanics (AM). It begins with its essential kinematico-inertial ingredients, such as kinetic energy and (system) acceleration or inertial “force” and their relation with the Euler-Lagrange operator (6.3.5g), and the forces involved. Then, the discussion moves to the synthesis of these concepts into the two basic principles of AM (Section 4.3): of d’ Alembert-Lagrange (LP) and of Lagrange-Hamel of the relaxation of the constraints (Lagrangean multipliers). These principles, in turn, produce all possible equations of motion: with reactions (kinetostatic) and without reactions (kinetic). The equivalent route based on the central equation of dynamics of Lagrange-Heun is also presented. The chapter ends with a discussion of the structure of the Lagrangean equations in holonomic variables and their geometrical interpretation in configuration space and a general treatment of energy rate, or power, equations. The above are presented in both particle vector (“raw” or “brute”) forms and system forms, in both holonomic and nonholonomic variables.*