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Lagrange Equations: Kinetic Energy of a Particle

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There is a case in which a bead is constrained to move on a wire shaped like a parabola. Now consider the case of a point-like bead constrained to move on the surface of a parabolic cup, whose equation, in cylindrical coordinates, is given by z = br2. Write down the kinetic energy of the particle and the generalized forces. Use the Lagrangian equations to find the equations of motion.

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This response provides a tutorial on how to write down the kinetic energy of a particle and the generalized forces for a bead forced to move on the surface of a parabolic cup.

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