Find curvature between the two track segments and aparameterization of the curve but the curvatures where pieces oftrack come together cannot differ by more t
han 1%. Lastly, find the total length of the final track.
Hints:
-To find a curve whose curvature increases linearly begin withk(s)=s (a linear increase with slope 1, with s representing arclength) and work backwards to find the vector function r(s).
-the unit tangent vector T(s) is a unit vector
T(s)=<cos(theta(s)),sin(theta(s))> for somefunction theta(s).
-use taylor series to compute an approximation to the transitioncurve.
-Finding the length of the transition curve will requirenumerical integration using a calculatoror computer.
Find curvature between the two track segments and a parameterization of the curve but the curvatures where pieces of track come together cannot differ by more t han 1%. Lastly, find the total length of the final track. Hints: -To find a curve whose curvature increases linearly begin with k(s)=s (a linear increase with slope 1, with s representing arc length) and work backwards to find the vector function r(s). -the unit tangent vector T(s) is a unit vector T(s)= for some function theta(s). -use taylor series to compute an approximation to the transition curve. -Finding the length of the transition curve will require numerical integration using a calculator or computer.
