I need help with a math problem. This is a hypothetical situaton:
Particle A and
Particle B have a mass
m and an attractive force acting on them proportional to the inverse square law. The force pulling them together is
F=-K/(r^2) (negative sign is a formality to make sure you know that the force is pulling the objects closer).
So we set up our equations before we differentiate. However this system encounters Lorenz dialations of mass (oh great).
so
m*a*c/ (c^2-v^2)^.5 = -K/r^2
m,
c (
c is the spesky speed of light), and
K are constants. [This
K will allow for the set up of using .5r (that's to the origin) because both particles will move exactly the same]
So remember, acceleration is the second derivative of position: d^2 r /dt^2 = a
SOLVE:
r(t) = ?
v(t) = r`(t) = ?
a(t) = r``(t) = ?
All those should be in terms of m, c, K and initial radius.
So there is some differential calc needed here and I went... Fuck Waffles! (-George Carlin).