ANALYTICAL MECHANICS
1.The second is, by definition,
the amount of time required for exactly 9,192,631,770 oscillations of a par-
ticular atomic transition of the cesium isotope of mass number 133.In our initial study of the science of motion,
mechanics, we shall assume that the physical space of ordinary experience is
adequately described by the three-dimensional mathematical space of Euclid-
ean geometry.VECTORS
the particle is an idealization that does not exist-even an electron has a
finite size but the idea is useful as an approximation of a small body, or
rather, one whose size is relatively unimportant in a particular discussion.The position of a point in such a coordinate system is specified by
three numbers or coordinates, x, y, and z. The coordinates of a moving point
change with time; that is, they are functions of the quantity t as measured
on our time scale.Physical Quantities and Units
The observational data of physics are expressed in terms of certain
fundamental entities called physical quantities-for example, length, time,
force, and so forth.The meter is now defined as
the distance occupied by exactly 1,650,763.73 wavelengths of light of the
orange spectrum line of the isotope krypton 86.The basic
type of coordinate system for our purpose is the Cartesian or rectangular
coordinate system, a set of three mutually perpendicular straight lines or
axes.The meter was formerly the
distance between two scratches on a platinum bar kept at the International
Bureau of Metric Standards, Sevres, France.Ve c t o r s
In any scientific theory, and in mechanics in particular, it
is necessary to begin with certain primitive concepts.A very useful concept in mechanics is the particle or mass point, an
entity that has mass' but does not have spatial extension.We shall further assume that space and time are distinct and inde-
pendent entities.The meter was formerly the
platinum iridium also kept at the International Bureau.Fundamental
Concepts.1.1.