120
DOC. 4 THEORY OF STATIC GRAVITATIONAL FIELD
For
a
material
point
that
moves
in
a
static
gravitational
field without
being
acted
upon by
external
forces
we
have
accordingly
=
o,
or
S
jj\jc2dt
-
dx2
-
dy2
-
dz2
j
=
0.
This shows
too-as
has been shown for the
ordinary theory
of
relativity by
[30]
Planck-that
the
equations
of
analytical
mechanics
have
a significance reaching
far
beyond
Newtonian mechanics. The Hamiltonian
equation,
which
was
the last
one
[31]
written
down,
gives
an
idea about how the
equations
of motion of the material
point
in
a dynamic gravitational
field
are
constructed.
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