chapter  6
52 Pages

Lagrangean Mechanics: Kinematics

WithJohn G. Papastavridis

This chapter begins our systematic treatment of Lagrangean or analytical mechanics (AM) by presenting the fundamental geometrical and kinematical concepts and equations of constrained and discrete (or discretizable) mechanical systems, such as position, velocity, kinematically admissible and virtual displacements’, geometrical or positional and kinematical or (here) velocity constraints and their integrability (holonomicity) or absence thereof (nonholonomicity), (including the transitivity equations and associated Hamel-Volterra coefficients (Section 3.13) and the fundamental integrability theorem of Frobenius) and stationarity (scleronomicity) or non-stationarity (rheonomicity); also their geometrical interpretation in physical and generalized (configuration/event) spaces, in both particle and system variables. The above constitute the indispensable underpinnings for the understanding of the next chapter on Lagrangean kinetics (i.e., equations of motion of the so-constrained systems). As with the rest of mechanics, the importance of kinematics can never be overestimated.*