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26 Nov 2019
Hi everyone, I've been struggling with this problem for a few daysnow, it has me stumped, anyone who can answer it with workingshown, all as lagrangian, is a legend.
Question:
A new half-pipe is being designed for sports, such as snowboardingand skateboading. Its cross section has the shape of a cycloiddefined by the parametric equations, x = a/4(2q +sin2q )and y = a/4(1-cos2q ), where -p/2 < q < p/2 anda is a constant.
Assuming the motion is constrained to the vertical plane, find theLagrangian of a particle of mass m that is free to slidealong the surface. Express the Lagrangian in terms of a substitutevariable s = asinq and find the equation ofmotion. Determine the frequency of oscillation of the motion.
Hi everyone, I've been struggling with this problem for a few daysnow, it has me stumped, anyone who can answer it with workingshown, all as lagrangian, is a legend.
Question:
A new half-pipe is being designed for sports, such as snowboardingand skateboading. Its cross section has the shape of a cycloiddefined by the parametric equations, x = a/4(2q +sin2q )and y = a/4(1-cos2q ), where -p/2 < q < p/2 anda is a constant.
Assuming the motion is constrained to the vertical plane, find theLagrangian of a particle of mass m that is free to slidealong the surface. Express the Lagrangian in terms of a substitutevariable s = asinq and find the equation ofmotion. Determine the frequency of oscillation of the motion.
