Question

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).

Answer 1

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.

Answer 2

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 = ( xŒ yŒŒ - xŒŒ yŒ ) / (vector V)^3

Answer 3

Wow that did not work...
Prove
(dphi/ds) = ( xprime*ydouble prime - xdoubleprime*yprime ) / (vector V)^3

Answer 4

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.

Answer 5

I am trying to prove the formula..