These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General Analytical Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity."
Now the kinetics of a medium in which the parts can have finite relative motions will lead to equations which are not linear - as, for example, those of hydrodynamics - and the phenomena will be far more complexly involved.
The subject is usually expounded under the two divisions of statics and kinetics, the former dealing with the conditions of rest or equilibrium and the latter with the phenomena of motion as affected by force.
Kinetics of a system of discrete particles.
Kinetics of a rigid body.
The proper significance of the principle of virtual work, and of its converse, will appear more clearly when we come to kinetics (~ 16); for the present it may be regarded merely as a compact and (for many purposes) highly convenient summary of the laws of equilibrium.
The question as to stability of equilibrium belongs essentially to kinetics; but we may state by anticipation that in cases where gravity is the only force which does work, the equilibrium of a body or system of bodies is stable only if the depth of the centre of gravity be a maximum.
The most important conception in kinetics is that of inertia.
Kinetics of a System of Discrete Particles.The momenta of the several particles constitute a system of localized vectors which, for purposes of resolving and taking moments, may be reduced like a system of forces in statics (~ 8).
Moving A xes of ReferenceFor the more general treatment of the kinetics of a rigid body it is usually convenient to adopt a system of moving axes.