posted by Mitch .
These questions relate to curvature problems.
a.Explain why (dÖ/ds) = (dÖ/dt) (dt/ds).
b.Explain why tanÖ = dy/dx, which equals (dy/dt) / (dx/dt).
I have to assume you know the chain rule.
if x is a function of t, and f is a function of x, then
df/dt=df/dx * dx/dt
this is a fundamental relationship in calculus.
I understand that much, but I still cannot derive the curvation equation..
a.Let x prime and x double prime be the first derivative and second derivatives of x with respect to t, and similarly for y. Show the following in true.
dƒ³/ds = ( xŒ yŒŒ - xŒŒ yŒ ) / (vector V)^3
Wow that did not work...
(dphi/ds) = ( xprime*ydouble prime - xdoubleprime*yprime ) / (vector V)^3
x prime. OK that is the first derivative of x with respect to ???
same for double prime. Your statement is just totally meaningless, it cant be proved unless it is understood.
I am trying to prove the formula..