>) Using r = 0(dr/de) write the energy equation in terms of r' = dr/de. c) For the remainder of this question the potential V = br². Using the change of variables w = 1/r², and then y =w-mE/L², show that the equation for the energy becomes the equation de 2 -4y² + 4D², ==
>) Using r = 0(dr/de) write the energy equation in terms of r' = dr/de. c) For the remainder of this question the potential V = br². Using the change of variables w = 1/r², and then y =w-mE/L², show that the equation for the energy becomes the equation de 2 -4y² + 4D², ==
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a is fine. please help b and c
Transcribed Image Text:(a) Starting with the radial orbital equation of motion in polar coordinates (r, 0)
L²
1 dV
m²p3
m dr
where L = mr²0 is the conserved angular momentum, show that the energy
+ m2 (rẻ)² + V
Ÿ –
and determine D².
E
-
m
dy
de
2
-j² +
is conserved.
(b) Using r = ġ(dr/d0) write the energy equation in terms of r' = dr/de.
(c) For the remainder of this question the potential V = br². Using the change of variables
1/r², and then y=w - mE/L², show that the equation for the energy becomes
the equation
W =
=
2
=
"
-4y² + 4D²,
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