
592 Appendix 2
and from Equation 4.1, we nd
dddand d
r
r
q
q
r
t
tr
r
q
q
i
i
j
j
j
n
i
i
i
j
=
∂
∂
+
∂
∂
=
∂
∂
=
∑
1
jj
j
n
i
r
t
=
∑
+
∂
∂
1
. (A2.20)
The partial derivatives in Equation A2.20 are themselves functions of the generalized coordinates q
i
and the time. As a result, the particle velocities have the following functional form:
rrqqqqi
ii nn
(,..., ;,..., ),,...,
11
1
NN.
Moreover, Equation A2.20 provides an explicit function of the indicated variables and shows that
in fact depends linearly on the generalized velocities
. Thus, we can readily evaluate the partial
derivative
/
to obtain
∂∂ =∂ ∂
rq
ij
. (A2.21)
Note that now the independent ...