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Word Count: 669
This new roller coaster as you will see has distinct problems at x 1005 1375 and 1495 At these points the track is uneven and has gaps or bumps For these to be dealt with the dimensionsfunctions provided to construct the coaster must be altered This is done by spliningsee Appendix-Definitions The functions that are being splined in addition to their first and second derivatives must be known The derivatives are taken to match the slopefirst derivativeand concavitysecond derivative at a point where two functions meet When those results dont match the roller coaster isnt as smooth as it should be This is where altering the current spline comes in handy After the splines are corrected the new track is operational smooth and doesnt jerk as it did before The roller coaster is now safe Shown in the following appendix is an in depth detailed analysis of the different problems associated to the coaster track and the repairssplines made to correct them Definitions Spline-a mathematical term used to describe in this case the curve that joins two functions at the nearest end points For example when you want to join a loop to a straight line to construct a loop the loop a spline is made to connect them First Derivative-this term is used to find many factors such as the slope of the tangent line to a curve the velocity of a particle and so on As far as roller coasters are concerned the first derivative is used to distinguish errors and the slope of the track Second Derivative-known as the derivative of the first derivative it is used to find the acceleration of a particle and the concavity of a curve Also used to identify problems with the roller coaster track Jerk-also known as the third derivative which is the derivative of the second derivative occurs when the second and third derivative dont match up on the track
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