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One simple way to model the motion of a roller coaster is to assume there is no friction, and that
nothing rolls. This is analogous to thinking of a bead moving down a wire fixed in space.
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We start with something simple: a straight line.
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A parabola: note the axes are not to scale.
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Getting a little more fancy, here's a cycloid.
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Joining two curves together, we have a Loop 'de Loop.
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Next we show a negative sine curve, computed two ways:
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1.) with position as a function of time
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2.) using the Hamiltonian method
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The following graphic shows both sine approximations simultaneously
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As a finale, here's a 3-D track.
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