
16 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Differentiating once with respect to time t yields the velocity
vrte
e
z
==
dd/
ˆˆˆ
ρρ
ρρ
. (1.25)
In order to calculate the derivatives of the unit vectors
and
with respect to time, we need
to rst establish relationships connecting them to
, and
. Such connecting formulas can be
established from a study of Figure 1.2a as we did for the plane polar coordinates. However, it is not
a trivial matter anymore. An alternative way is to rst nd the vectors that are tangential to the ρ-,
ϕ-, and z-curves. These vectors are given, respectively, by ∂r/∂ρ, ∂r/∂ϕ, and ∂r/∂z. Then, ...