Problem Outline: I'm trying to determine how to keep the distance between 2 cars on a (3D) roller coaster ride. Currently the front car moves away from the back car.(adsbygoogle = window.adsbygoogle || []).push({});

My current implementation uses a second order differential equation to model the acceleration of the cars at time t. The equation is as follows:

y'' = ((n^3 * H^2 * y' ^ 2 * sin(n * theta) - n*g*H) * cos(n * theta)) / (R^2 + n^2 * H^2 *cos^2(n * theta))

n = no. of hills,

R = radius of the track,

H = height of the hills (in metres)

theta = angle of revolution about the track

This ODE is numerically integrated using the Runge-Kutta method.

Information much appreciated. Any further information please do not hesitate to ask.

thanks.

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# Homework Help: Determining an Equation of Motion

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