DOC.
1
MECHANICS LECTURE NOTES
107
do}
dt
+qo
-
ro
~o)
sin
(po
=
L
n
z y
y
onsina
-
-
osin(p
sin
a
on
=
-M
sin
a
0 dt
o)
is
small compared with
-.
Hence
M
=
a0-
can
be considerable.
y
dt 0 dt
Introduction of
the
Kinetic
Potential[68]
[p. 107]
p
=
d
v
dt
'
dL*
dpi
+
0(11
-
L)
dP"
We set II
-
L
=
H.
Because II
is
independent
of
p'v,
we
can
then
write
the
equation
in
the
following way
P
+
-
v
dt
ffl
M,
dH
=
0
Thus,
the
knowledge
of
a
single
function
is
all
that
is
needed
to
determine the
motion of
a system.
One
calls
H the kinetic
potential.
If
the
function H
is
introduced
into Hamilton's
principle,
the latter
assumes
the form
x
J
(5H
-
PvlPv)dt
=
0
This
equation is
a
direct
consequence
of
the
one just given.
If
we
denote
by
Pv
the
force
applied
by
the
system
to
the environment rather than the
force
applied
by
the
environment
to
the
system,
then
Pv
has to
be
replaced
by
-
P-v,
so
that
one
has to set
p-
_
d
v
Jt
'dHS
dpi
+
™
=
0
dp