Consider a particle of mass (m) moving in two dimensions in the (x-y) plane, constrained to a
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Consider a particle of mass \(m\) moving in two dimensions in the \(x-y\) plane, constrained to a rail-track whose shape is described by an arbitrary function \(y=f(x)\). There is no gravity acting on the particle.
(a) Write the Lagrangian in terms of the \(x\) degree of freedom only.
(b) Consider some general transformation of the form
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