z12,=0.5x,? X2 Z2 A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above. Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion in terms of the distance from the lowest point, q1 = x2.
z12,=0.5x,? X2 Z2 A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above. Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion in terms of the distance from the lowest point, q1 = x2.
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this is done by the Lagrangian method.
take a variation of kinetic energy expressions and same with potential energy and then combine it with virtual work to get the equation of motion.
Variation calculus is needed.
If you can get a differential equation representing motion by another method then it's cool.
Transcribed Image Text:z12,=0.5x,?
X2
Z2
A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above.
Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion in
terms of the distance from the lowest point, q1 = 12.
a. What is the kinetic energy of the cart?
b. What is the potential energy of the cart?
c. What is the equation of motion for the cart?
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