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A bead slides on the inner surface of a paraboloid z = Cr*, as shown in Figure 2. C is a constant, and r is the distance of the bead from the z axis. By letting the potential energy be zero at the origin, find the bead's (a) Lagrange's equations of motion, and (b) Hamilton's equation of motion.

A bead slides on the inner surface of a paraboloid z = Cr*, as shown in Figure 2. C is a constant, and r is the distance of the bead from the z axis. By letting the potential energy be zero at the origin, find the bead's (a) Lagrange's equations of motion, and (b) Hamilton's equation of motion.

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This is a question from classical mechanics. Please answer only whenyou are sure.

A bead slides on the inner surface of a paraboloid z = C r*, as shown in Figure 2. C is a constant, and r is the distance of the bead from the z axis. By letting the potential energy be zero at the origin, find the bead's (a) Lagrange's equations of motion, and (b) Hamilton's equation of motion. Figure 2
Transcribed Image Text:A bead slides on the inner surface of a paraboloid z = C r*, as shown in Figure 2. C is a constant, and r is the distance of the bead from the z axis. By letting the potential energy be zero at the origin, find the bead's (a) Lagrange's equations of motion, and (b) Hamilton's equation of motion. Figure 2
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