A bead can slide on a straight wire which is always in the vertical plane. C is point on wire and wire is moving so the line joining origin O and Point C is rotated in the vertical plane with constant angular velocity ω. (a) Find appropriate generalised coordinates, Lagrangian, and the Euler-Lagrange equations and solve it for the position of the bead. (b) Find Hamiltonain. Comment on the total energy of the system.

A bead can slide on a straight wire which is always in the vertical plane. C is point on wire and wire is moving so the line joining origin O and Point C is rotated in the vertical plane with constant angular velocity ω. (a) Find appropriate generalised coordinates, Lagrangian, and the Euler-Lagrange equations and solve it for the position of the bead. (b) Find Hamiltonain. Comment on the total energy of the system.

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Question

A bead can slide on a straight wire which is always in the vertical plane. C is point on wire and wire is moving so the line joining origin O and Point C is rotated in the vertical plane with constant angular velocity ω.
(a) Find appropriate generalised coordinates, Lagrangian, and the Euler-Lagrange equations and solve it for the position of the bead.
(b) Find Hamiltonain. Comment on the total energy of the system.

Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.

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