
check this math please
out of the goodness of your heart, i want to make sure i derived these nasty equations properly. I'm trying to find the instantaneous force of gravity on a particle that has come to rest on the parametric object represented by these equations:
X = 10cos(t) + (cos(t) * 2sin(9t))
Y = 10sin(t) + (sin(t) * 2sin(9t))
It's a sine wave that travels around a circle. The particle comes to rest at t=1.04, or (5,8.66). These are the equations i get for the derivatives of x and y using product and chain rules:
X’ = 10sin(t) – (sin(t) * 2sin(9t)) + (cos(t) * 18cos(9t))
Y’ = 10cos(t) + (cos(t) * 2sin(9t)) + (sin(t) * 18cos(9t))
and then the slope I get (with derivative of y with respect to t divided by the derivative of x with respect to t) is .58104, which is completely reasonable. I've drawn a line tangent to the curve at that point, and it touches that point, and it *looks* like it really is a tangent, but I just want to make sure I derived x and y properly(and yes im in radians).
EDIT: Okay, I can't delete this crap, but I basically know it works, so, yeah, beans