Mechanics of Material Forces

The Study of Kinematics and Kinetics of Rigid Bodies

“Modern Introductory Mechanics, Part II” is a continuation of the coverage of topics in classical mechanics found in Part I. The text builds on the previous material and maintains the same spirit of directness and rigor. It is designed to round out the coverage of the important topics in the field, leading to more advanced treatments. Subject matter includes central forces, scattering, non-internal reference frames, rigid bodies, coupled oscillations and special relativity. As in Part I, the many homework problems are directly associated with the development of ideas and topics in the text.

The motion of any body depends both on its characteristics and the forces acting on it. Although taking into account all possible properties makes the equations too complex to solve, sometimes it is possible to consider only the properties that have the greatest in?uence on the motion. Models of ideals bodies, which contain only the most relevant properties, can be studied using the tools of mathematical physics. Adding more properties into a model makes it more realistic, but it also makes the motion problem harder to solve. In order to highlight the above statements, let us ?rst suppose that a systemS ofN unconstrainedbodiesC ,i=1,. . . ,N,issu?cientlydescribed i by the model of N material points whenever the bodies have negligible dimensions with respect to the dimensions of the region containing the trajectories. ThismeansthatallthephysicalpropertiesofC thatin?uence i the motion are expressed by a positive number, themass m , whereas the i position of C with respect to a frame I is given by the position vector i r (t) versus time. To determine the functionsr (t), one has to integrate the i i following system of Newtonian equations: m¨ r =F ?f (r ,. . . ,r ,r ? ,. . . ,r ? ,t), i i i i 1 N 1 N i=1,

A Comprehensive Journey from Coulomb’s Law to Advanced Electrostatic Systems