DOC.
1
MECHANICS LECTURE NOTES
111
n-
=
-
dW
dt
work
delivered
=
work
of the electromotive
force.
The
previous
page
follows
Limit
of
the
applicability
of
the
principle
of least action
dH
dt
-I
canonical equations
d_(dL\
d(U-L)
=
v
dt
WJ
dp
=
^divÖPv
+
^
qv3p'v
HL
-
I
qvp'v)
y
'
T
=
I
%rP,'
I
P'M,
Pv^
dt
\dp[
d
fdH\
dH
+
dp
-T7
öH
= YJ
Z
4*SP
dH
S(H
+
pvqv)
=
Z^T^P
v
J
CPv
r
T
Z
P'M
dT
_
dH dT
dpv
dpv dqv
=
t,P\
dqv
_
p
_
dT
dt
v
dp
T
=
0
+
L
dp,^
dT
dt
dqv
[p. 111]
in
case
of
ponderable
mechanics
=
E.
If
T
is
viewed, secondly,
as
function of
pv
&
qv,
then
xt
r*
dT»
dT
Hence,
we
have
8L
m
dT
dp.
dpv
P\
=
dT
dqv
Therefore,
dp
dt
3T
dqv