202 
Of ane SOEREN) 
==, b= GS 
dt dt dt 
where r ov 
One of the equations of motion is 
d (OL 
hey Bomac VE 
or 
r? sin? J p 
en =*00nt., 
L 
which proves that p‚ once being zero, keeps that value. 
Now, as we can always choose 9 and p in such a way that 
p becomes zero for a certain value of ¢ and as p will then always 
remain zero, the motion takes place in a plane. 
We choose the coordinates in such a manner, that this plane 
TL 
becomes the plane # = = Then (9) passes into 
a r? 
L= VA Ag EE ee rcp" 
r a 
jk 
r 
The equations of motion are 
d (OL) d (ol) dL 
dt G)=e dt (= or 
From these two it follows that 
d ( . OL . 0 =) 
—|{ Lr non \|.== 0 
dt Op og 
or 
(10) 
(11) 
(12) 
Instead of the two equations (11) we may consider the system, 
consisting of (11) and (412). The two systems are equivalent only 
in case r=/—0; so for the circular motion we shall have to return 
to the second equation (10). 
We now obtain 
a 
i eres 
r rp 
——— == CONS, — = const., 
L L 
and so 
